MTH4152 concept map

Concept map MTH 4152

Table and graphs

• I can build and interpret a frequency table
• I can build and interpret a bar graph (for qualitative data) or a histogram (for quantitative data)
• I can build and interpret a stem-and-leaf graph

Mean and mean deviation

• I can calculate mean, mean deviation and range from:
  • a data distribution
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can find a missing value from its mean and its data distribution
• I can interpret mean, mean deviation and range

Percentile rank

• I can calculate percentile rank from:
  • a complete or incomplete data distribution
  • descriptions
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can interpret a percentile rank
• I can calculate a value from its percentile rank

Scatter plot

Example

Linear regression

Draw a straight line representing the overall pattern seen in the scatter plot Example:

Correlation coefficient

Use the box method to estimate the linear correlation coefficient (r) OR Use technology to calculate the linear correlation coefficient (r) You will be provided with this formula and this table in your exam

Frequency table

I can build and interpret frequency tables

Bar/histogram

I can create and interpret a bar graph (for a qualitative data) I can create and interpret a histogram (for a quantitative data)

Stem-and-leaf

I can build and interpret a stem-and-leaf graph

• One sided or two sided
• Whole numbers or decimal numbers

Examples: Cost of accessories ($) for cars or vans

Mean & mean deviation

I can calculate mean, mean deviation and range from:

• a data distribution
• a frequency table or a histogram
• a stem-and-leaf graph

To calculate mean

1. add up all the values
2. divide the sum (from the first step) by the total number of values

To calculate mean deviation

1. calculate the difference of each value from the mean (disregard if the difference is positive or negative)
2. add up all the differences
3. divide the sum (from the second step) by the total number of values

I can interpret mean and mean deviation (so mean and mean deviation from one group can be compared to the mean and mean deviation from another group)

• mean is an average value of a group. If the mean is different then it can mean many values in two groups are different.
• mean deviation is a measure of dispersion. If a group has a larger mean deviation, it means its values are different from each other.

Find missing value from its mean

Example: Find the missing value by reversing the procedure for calculating the mean.

1. Multiply the mean by the total number of values (including the missing value)70 x 18 = 1260
2. Subtract the sum from step 1 with all known values. The left over will be the missing value1260 - 44 - 46 - 47 - 49 - 63 - 64 - 66 - 68 - 68 - 72 - 72 - 75 - 76 - 81 - 84 - 88 - 106 = 91

Answer: missing value is 91

Range

Range is the the largest value minus the smallest value. Example: number of friends on Facebook Range is 138-21 = 117 Example: Range is 90-60=30 Example: Range = 30-3= 27 Range is a measure of dispersion. A larger value for range means there are more variations within the dataset.

Percentile rank

I can calculate percentile rank from:

• a complete or incomplete data distribution
• descriptions
• a frequency table or a histogram
• a stem-and-leaf graph

I can interpret a percentile rank Example: Calculate the percentile rank of 5 as the number in the set. N smaller = 9 (the first 4 bars' heights = 1+2+4+2)N equal = 1 (the bar corresponds to the value '5' has height of 1)N total = 11 (heights of all bars = 1+2+4+2+1+1=11)R100 = (9 + 1/2) / 11 * 100 = (9 + 0.5) / 11 * 100 = 9.5 / 11 * 100 = 86.36 ~ 87th percentile rank

Find missing value from its percentile

I can calculate a value from its percentile rank Example: Reverse the percentile rank calculation.

1. 88 percentile divided by 100 = 0.88
2. 0.88 times the total number of values, 0.88x20=17.6
3. Assuming N= is just one. So N=/2 = 0.5. Plus 0.5 becomes minus 0.5 when reversing the calculation17.6 - 0.5 = 17.1 ~ 17
4. There are 17 number less than the value in question.The answer is therefore $35

Scatter plot

• Graphing area should be square-ish
• Each axis (x and y) can use the same or different intervals
• Each axis (x and y) can start at 0 or not.
• Each axis should be labelled
• The graph should have a title

Regression line

Draw a straight line representing the overall pattern seen in the scatter plot Ignore the outlier(s) - one or more points that are clearly far away from the rest of the data. *Outlier will be VERY OBVIOUS in this course. Example:

Linear equation

Sign & strength

Positive correlations (blue), from strong to weak (top to bottom). Negative correlation (orange), from strong to weak (top to bottom)

Box method

Draw a rectangular box to surround all the data points* *excluding the outlier(s) Then measure the width and length of the box using your rule. Use the formula to estimate the correlation coefficient.

Interpretation

A correlation with a strong correlation coefficient would mean

• the linear regression line is very close to most if not all of the data points
• the relationship between the two variables can be very well modelled using the linear equation
• one variable strongly affect the other variable
• the relationship between the two variables can be predicated accurately

Sign of correlation

• I can create a contingency table (also called a correlation table).
• I can determine the sign of the correlation from a contingency table.

Example of a positive correlation Example of a negative correlation

One variable

Analyses on one variable on a time, including:

• Frequency table, bar graph and histogram
• Stem-and-leaf graph
• Mean, mean deviation and range
• Percentile rank

Two variables

Focusing on how one variable affects the other variable. Usually the first column/row is:

• the independent variable
• x or the horizontal axis on the cartesian graph

And the second column/row is:

• the dependent variable
• y or the vertical axis on the cartesian graph

Statistics

Vocabulary

• Population means the group of individuals or items of interests in a statistical study
• Sample means a part of the population
• Qualitative data are responses that describes feelings etc.
• Quantitative data are numerical values from counting or measuring
  • Quantitative and discrete data are from counting
  • Quantitative and continuous data are from measuring

Contingency table

Example:

Exam

Click everywhere for more information!

Exam

Explicit Evaluation of Knowledge (20%)- 4 questions - click to see individual examples

Task questions (80%)- 3 task questions- click to see individual examples

Calculate

Graph / interpret

Analysis for one variable

Analysis for two variables

Concept map MTH 4152

You could be asked to calculate:mean, mean deviation and range or percentile rank

Using:

• a series of values
• a frequency table
• a histogram
• a stem-and-leaf graph

Concept map MTH 4152

Table and graphs

• I can build and interpret a frequency table
• I can build and interpret a bar graph (for qualitative data) or a histogram (for quantitative data)
• I can build and interpret a stem-and-leaf graph

Mean and mean deviation

• I can calculate mean, mean deviation and range from:
  • a data distribution
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can find a missing value from its mean and its data distribution
• I can interpret mean, mean deviation and range

Percentile rank

• I can calculate percentile rank from:
  • a complete or incomplete data distribution
  • descriptions
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can interpret a percentile rank
• I can calculate a value from its percentile rank

Scatter plot

Example

Linear regression

Draw a straight line representing the overall pattern seen in the scatter plot Example:

Correlation coefficient

Use the box method to estimate the linear correlation coefficient (r) OR Use technology to calculate the linear correlation coefficient (r) You will be provided with this formula and this table in your exam

Frequency table

I can build and interpret frequency tables

Bar/histogram

I can create and interpret a bar graph (for a qualitative data) I can create and interpret a histogram (for a quantitative data)

Stem-and-leaf

I can build and interpret a stem-and-leaf graph

• One sided or two sided
• Whole numbers or decimal numbers

Examples: Cost of accessories ($) for cars or vans

Mean & mean deviation

I can calculate mean, mean deviation and range from:

• a data distribution
• a frequency table or a histogram
• a stem-and-leaf graph

To calculate mean

1. add up all the values
2. divide the sum (from the first step) by the total number of values

To calculate mean deviation

1. calculate the difference of each value from the mean (disregard if the difference is positive or negative)
2. add up all the differences
3. divide the sum (from the second step) by the total number of values

I can interpret mean and mean deviation (so mean and mean deviation from one group can be compared to the mean and mean deviation from another group)

• mean is an average value of a group. If the mean is different then it can mean many values in two groups are different.
• mean deviation is a measure of dispersion. If a group has a larger mean deviation, it means its values are different from each other.

Find missing value from its mean

Example: Find the missing value by reversing the procedure for calculating the mean.

1. Multiply the mean by the total number of values (including the missing value)70 x 18 = 1260
2. Subtract the sum from step 1 with all known values. The left over will be the missing value1260 - 44 - 46 - 47 - 49 - 63 - 64 - 66 - 68 - 68 - 72 - 72 - 75 - 76 - 81 - 84 - 88 - 106 = 91

Answer: missing value is 91

Range

Range is the the largest value minus the smallest value. Example: number of friends on Facebook Range is 138-21 = 117 Example: Range is 90-60=30 Example: Range = 30-3= 27 Range is a measure of dispersion. A larger value for range means there are more variations within the dataset.

Percentile rank

I can calculate percentile rank from:

• a complete or incomplete data distribution
• descriptions
• a frequency table or a histogram
• a stem-and-leaf graph

I can interpret a percentile rank Example: Calculate the percentile rank of 5 as the number in the set. N smaller = 9 (the first 4 bars' heights = 1+2+4+2)N equal = 1 (the bar corresponds to the value '5' has height of 1)N total = 11 (heights of all bars = 1+2+4+2+1+1=11)R100 = (9 + 1/2) / 11 * 100 = (9 + 0.5) / 11 * 100 = 9.5 / 11 * 100 = 86.36 ~ 87th percentile rank

Find missing value from its percentile

I can calculate a value from its percentile rank Example: Reverse the percentile rank calculation.

1. 88 percentile divided by 100 = 0.88
2. 0.88 times the total number of values, 0.88x20=17.6
3. Assuming N= is just one. So N=/2 = 0.5. Plus 0.5 becomes minus 0.5 when reversing the calculation17.6 - 0.5 = 17.1 ~ 17
4. There are 17 number less than the value in question.The answer is therefore $35

Scatter plot

• Graphing area should be square-ish
• Each axis (x and y) can use the same or different intervals
• Each axis (x and y) can start at 0 or not.
• Each axis should be labelled
• The graph should have a title

Regression line

Draw a straight line representing the overall pattern seen in the scatter plot Ignore the outlier(s) - one or more points that are clearly far away from the rest of the data. *Outlier will be VERY OBVIOUS in this course. Example:

Linear equation

Sign & strength

Positive correlations (blue), from strong to weak (top to bottom). Negative correlation (orange), from strong to weak (top to bottom)

Box method

Draw a rectangular box to surround all the data points* *excluding the outlier(s) Then measure the width and length of the box using your rule. Use the formula to estimate the correlation coefficient.

Interpretation

A correlation with a strong correlation coefficient would mean

• the linear regression line is very close to most if not all of the data points
• the relationship between the two variables can be very well modelled using the linear equation
• one variable strongly affect the other variable
• the relationship between the two variables can be predicated accurately

Sign of correlation

• I can create a contingency table (also called a correlation table).
• I can determine the sign of the correlation from a contingency table.

Example of a positive correlation Example of a negative correlation

One variable

Analyses on one variable on a time, including:

• Frequency table, bar graph and histogram
• Stem-and-leaf graph
• Mean, mean deviation and range
• Percentile rank

Two variables

Focusing on how one variable affects the other variable. Usually the first column/row is:

• the independent variable
• x or the horizontal axis on the cartesian graph

And the second column/row is:

• the dependent variable
• y or the vertical axis on the cartesian graph

Statistics

Vocabulary

• Population means the group of individuals or items of interests in a statistical study
• Sample means a part of the population
• Qualitative data are responses that describes feelings etc.
• Quantitative data are numerical values from counting or measuring
  • Quantitative and discrete data are from counting
  • Quantitative and continuous data are from measuring

Contingency table

Example:

Concept map MTH 4152

You could be asked to create and/or interpret:

• a contingency table
• a stem-and-leaf graph
• one or more scatter plots

Concept map MTH 4152

Table and graphs

• I can build and interpret a frequency table
• I can build and interpret a bar graph (for qualitative data) or a histogram (for quantitative data)
• I can build and interpret a stem-and-leaf graph

Mean and mean deviation

• I can calculate mean, mean deviation and range from:
  • a data distribution
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can find a missing value from its mean and its data distribution
• I can interpret mean, mean deviation and range

Percentile rank

• I can calculate percentile rank from:
  • a complete or incomplete data distribution
  • descriptions
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can interpret a percentile rank
• I can calculate a value from its percentile rank

Scatter plot

Example

Linear regression

Draw a straight line representing the overall pattern seen in the scatter plot Example:

Correlation coefficient

Use the box method to estimate the linear correlation coefficient (r) OR Use technology to calculate the linear correlation coefficient (r) You will be provided with this formula and this table in your exam

Frequency table

I can build and interpret frequency tables

Bar/histogram

I can create and interpret a bar graph (for a qualitative data) I can create and interpret a histogram (for a quantitative data)

Stem-and-leaf

I can build and interpret a stem-and-leaf graph

• One sided or two sided
• Whole numbers or decimal numbers

Examples: Cost of accessories ($) for cars or vans

Mean & mean deviation

I can calculate mean, mean deviation and range from:

• a data distribution
• a frequency table or a histogram
• a stem-and-leaf graph

To calculate mean

1. add up all the values
2. divide the sum (from the first step) by the total number of values

To calculate mean deviation

1. calculate the difference of each value from the mean (disregard if the difference is positive or negative)
2. add up all the differences
3. divide the sum (from the second step) by the total number of values

I can interpret mean and mean deviation (so mean and mean deviation from one group can be compared to the mean and mean deviation from another group)

• mean is an average value of a group. If the mean is different then it can mean many values in two groups are different.
• mean deviation is a measure of dispersion. If a group has a larger mean deviation, it means its values are different from each other.

Find missing value from its mean

Example: Find the missing value by reversing the procedure for calculating the mean.

1. Multiply the mean by the total number of values (including the missing value)70 x 18 = 1260
2. Subtract the sum from step 1 with all known values. The left over will be the missing value1260 - 44 - 46 - 47 - 49 - 63 - 64 - 66 - 68 - 68 - 72 - 72 - 75 - 76 - 81 - 84 - 88 - 106 = 91

Answer: missing value is 91

Range

Range is the the largest value minus the smallest value. Example: number of friends on Facebook Range is 138-21 = 117 Example: Range is 90-60=30 Example: Range = 30-3= 27 Range is a measure of dispersion. A larger value for range means there are more variations within the dataset.

Percentile rank

I can calculate percentile rank from:

• a complete or incomplete data distribution
• descriptions
• a frequency table or a histogram
• a stem-and-leaf graph

I can interpret a percentile rank Example: Calculate the percentile rank of 5 as the number in the set. N smaller = 9 (the first 4 bars' heights = 1+2+4+2)N equal = 1 (the bar corresponds to the value '5' has height of 1)N total = 11 (heights of all bars = 1+2+4+2+1+1=11)R100 = (9 + 1/2) / 11 * 100 = (9 + 0.5) / 11 * 100 = 9.5 / 11 * 100 = 86.36 ~ 87th percentile rank

Find missing value from its percentile

I can calculate a value from its percentile rank Example: Reverse the percentile rank calculation.

1. 88 percentile divided by 100 = 0.88
2. 0.88 times the total number of values, 0.88x20=17.6
3. Assuming N= is just one. So N=/2 = 0.5. Plus 0.5 becomes minus 0.5 when reversing the calculation17.6 - 0.5 = 17.1 ~ 17
4. There are 17 number less than the value in question.The answer is therefore $35

Scatter plot

• Graphing area should be square-ish
• Each axis (x and y) can use the same or different intervals
• Each axis (x and y) can start at 0 or not.
• Each axis should be labelled
• The graph should have a title

Regression line

Draw a straight line representing the overall pattern seen in the scatter plot Ignore the outlier(s) - one or more points that are clearly far away from the rest of the data. *Outlier will be VERY OBVIOUS in this course. Example:

Linear equation

Sign & strength

Positive correlations (blue), from strong to weak (top to bottom). Negative correlation (orange), from strong to weak (top to bottom)

Box method

Draw a rectangular box to surround all the data points* *excluding the outlier(s) Then measure the width and length of the box using your rule. Use the formula to estimate the correlation coefficient.

Interpretation

A correlation with a strong correlation coefficient would mean

• the linear regression line is very close to most if not all of the data points
• the relationship between the two variables can be very well modelled using the linear equation
• one variable strongly affect the other variable
• the relationship between the two variables can be predicated accurately

Sign of correlation

• I can create a contingency table (also called a correlation table).
• I can determine the sign of the correlation from a contingency table.

Example of a positive correlation Example of a negative correlation

One variable

Analyses on one variable on a time, including:

• Frequency table, bar graph and histogram
• Stem-and-leaf graph
• Mean, mean deviation and range
• Percentile rank

Two variables

Focusing on how one variable affects the other variable. Usually the first column/row is:

• the independent variable
• x or the horizontal axis on the cartesian graph

And the second column/row is:

• the dependent variable
• y or the vertical axis on the cartesian graph

Statistics

Vocabulary

• Population means the group of individuals or items of interests in a statistical study
• Sample means a part of the population
• Qualitative data are responses that describes feelings etc.
• Quantitative data are numerical values from counting or measuring
  • Quantitative and discrete data are from counting
  • Quantitative and continuous data are from measuring

Contingency table

Example:

Concept map MTH 4152

You could be asked to perform analysis for one variable, which could involve:

• calculating and interpreting mean, mean deviation and range
• calculating and interpreting percentile rank

Concept map MTH 4152

Table and graphs

• I can build and interpret a frequency table
• I can build and interpret a bar graph (for qualitative data) or a histogram (for quantitative data)
• I can build and interpret a stem-and-leaf graph

Mean and mean deviation

• I can calculate mean, mean deviation and range from:
  • a data distribution
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can find a missing value from its mean and its data distribution
• I can interpret mean, mean deviation and range

Percentile rank

• I can calculate percentile rank from:
  • a complete or incomplete data distribution
  • descriptions
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can interpret a percentile rank
• I can calculate a value from its percentile rank

Scatter plot

Example

Linear regression

Draw a straight line representing the overall pattern seen in the scatter plot Example:

Correlation coefficient

Use the box method to estimate the linear correlation coefficient (r) OR Use technology to calculate the linear correlation coefficient (r) You will be provided with this formula and this table in your exam

Frequency table

I can build and interpret frequency tables

Bar/histogram

I can create and interpret a bar graph (for a qualitative data) I can create and interpret a histogram (for a quantitative data)

Stem-and-leaf

I can build and interpret a stem-and-leaf graph

• One sided or two sided
• Whole numbers or decimal numbers

Examples: Cost of accessories ($) for cars or vans

Mean & mean deviation

I can calculate mean, mean deviation and range from:

• a data distribution
• a frequency table or a histogram
• a stem-and-leaf graph

To calculate mean

1. add up all the values
2. divide the sum (from the first step) by the total number of values

To calculate mean deviation

1. calculate the difference of each value from the mean (disregard if the difference is positive or negative)
2. add up all the differences
3. divide the sum (from the second step) by the total number of values

I can interpret mean and mean deviation (so mean and mean deviation from one group can be compared to the mean and mean deviation from another group)

• mean is an average value of a group. If the mean is different then it can mean many values in two groups are different.
• mean deviation is a measure of dispersion. If a group has a larger mean deviation, it means its values are different from each other.

Find missing value from its mean

Example: Find the missing value by reversing the procedure for calculating the mean.

1. Multiply the mean by the total number of values (including the missing value)70 x 18 = 1260
2. Subtract the sum from step 1 with all known values. The left over will be the missing value1260 - 44 - 46 - 47 - 49 - 63 - 64 - 66 - 68 - 68 - 72 - 72 - 75 - 76 - 81 - 84 - 88 - 106 = 91

Answer: missing value is 91

Range

Range is the the largest value minus the smallest value. Example: number of friends on Facebook Range is 138-21 = 117 Example: Range is 90-60=30 Example: Range = 30-3= 27 Range is a measure of dispersion. A larger value for range means there are more variations within the dataset.

Percentile rank

I can calculate percentile rank from:

• a complete or incomplete data distribution
• descriptions
• a frequency table or a histogram
• a stem-and-leaf graph

I can interpret a percentile rank Example: Calculate the percentile rank of 5 as the number in the set. N smaller = 9 (the first 4 bars' heights = 1+2+4+2)N equal = 1 (the bar corresponds to the value '5' has height of 1)N total = 11 (heights of all bars = 1+2+4+2+1+1=11)R100 = (9 + 1/2) / 11 * 100 = (9 + 0.5) / 11 * 100 = 9.5 / 11 * 100 = 86.36 ~ 87th percentile rank

Find missing value from its percentile

I can calculate a value from its percentile rank Example: Reverse the percentile rank calculation.

1. 88 percentile divided by 100 = 0.88
2. 0.88 times the total number of values, 0.88x20=17.6
3. Assuming N= is just one. So N=/2 = 0.5. Plus 0.5 becomes minus 0.5 when reversing the calculation17.6 - 0.5 = 17.1 ~ 17
4. There are 17 number less than the value in question.The answer is therefore $35

Scatter plot

• Graphing area should be square-ish
• Each axis (x and y) can use the same or different intervals
• Each axis (x and y) can start at 0 or not.
• Each axis should be labelled
• The graph should have a title

Regression line

Draw a straight line representing the overall pattern seen in the scatter plot Ignore the outlier(s) - one or more points that are clearly far away from the rest of the data. *Outlier will be VERY OBVIOUS in this course. Example:

Linear equation

Sign & strength

Positive correlations (blue), from strong to weak (top to bottom). Negative correlation (orange), from strong to weak (top to bottom)

Box method

Draw a rectangular box to surround all the data points* *excluding the outlier(s) Then measure the width and length of the box using your rule. Use the formula to estimate the correlation coefficient.

Interpretation

A correlation with a strong correlation coefficient would mean

• the linear regression line is very close to most if not all of the data points
• the relationship between the two variables can be very well modelled using the linear equation
• one variable strongly affect the other variable
• the relationship between the two variables can be predicated accurately

Sign of correlation

• I can create a contingency table (also called a correlation table).
• I can determine the sign of the correlation from a contingency table.

Example of a positive correlation Example of a negative correlation

One variable

Analyses on one variable on a time, including:

• Frequency table, bar graph and histogram
• Stem-and-leaf graph
• Mean, mean deviation and range
• Percentile rank

Two variables

Focusing on how one variable affects the other variable. Usually the first column/row is:

• the independent variable
• x or the horizontal axis on the cartesian graph

And the second column/row is:

• the dependent variable
• y or the vertical axis on the cartesian graph

Statistics

Vocabulary

• Population means the group of individuals or items of interests in a statistical study
• Sample means a part of the population
• Qualitative data are responses that describes feelings etc.
• Quantitative data are numerical values from counting or measuring
  • Quantitative and discrete data are from counting
  • Quantitative and continuous data are from measuring

Contingency table

Example:

Concept map MTH 4152

You could be asked to perform the analysis for two variables, which could involve:

• creating scatter plots
• drawing a linear regression line and determining its equation
• using that equation
• using the box method to estimate a correlation coefficient value
• interpret the correlation coefficient value

Concept map MTH 4152

Table and graphs

• I can build and interpret a frequency table
• I can build and interpret a bar graph (for qualitative data) or a histogram (for quantitative data)
• I can build and interpret a stem-and-leaf graph

Mean and mean deviation

• I can calculate mean, mean deviation and range from:
  • a data distribution
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can find a missing value from its mean and its data distribution
• I can interpret mean, mean deviation and range

Percentile rank

• I can calculate percentile rank from:
  • a complete or incomplete data distribution
  • descriptions
  • a frequency table or a histogram
  • a stem-and-leaf graph
• I can interpret a percentile rank
• I can calculate a value from its percentile rank

Scatter plot

Example

Linear regression

Draw a straight line representing the overall pattern seen in the scatter plot Example:

Correlation coefficient

Use the box method to estimate the linear correlation coefficient (r) OR Use technology to calculate the linear correlation coefficient (r) You will be provided with this formula and this table in your exam

Frequency table

I can build and interpret frequency tables

Bar/histogram

I can create and interpret a bar graph (for a qualitative data) I can create and interpret a histogram (for a quantitative data)

Stem-and-leaf

I can build and interpret a stem-and-leaf graph

• One sided or two sided
• Whole numbers or decimal numbers

Examples: Cost of accessories ($) for cars or vans

Mean & mean deviation

I can calculate mean, mean deviation and range from:

• a data distribution
• a frequency table or a histogram
• a stem-and-leaf graph

To calculate mean

1. add up all the values
2. divide the sum (from the first step) by the total number of values

To calculate mean deviation

1. calculate the difference of each value from the mean (disregard if the difference is positive or negative)
2. add up all the differences
3. divide the sum (from the second step) by the total number of values

I can interpret mean and mean deviation (so mean and mean deviation from one group can be compared to the mean and mean deviation from another group)

• mean is an average value of a group. If the mean is different then it can mean many values in two groups are different.
• mean deviation is a measure of dispersion. If a group has a larger mean deviation, it means its values are different from each other.

Find missing value from its mean

Example: Find the missing value by reversing the procedure for calculating the mean.

1. Multiply the mean by the total number of values (including the missing value)70 x 18 = 1260
2. Subtract the sum from step 1 with all known values. The left over will be the missing value1260 - 44 - 46 - 47 - 49 - 63 - 64 - 66 - 68 - 68 - 72 - 72 - 75 - 76 - 81 - 84 - 88 - 106 = 91

Answer: missing value is 91

Range

Range is the the largest value minus the smallest value. Example: number of friends on Facebook Range is 138-21 = 117 Example: Range is 90-60=30 Example: Range = 30-3= 27 Range is a measure of dispersion. A larger value for range means there are more variations within the dataset.

Percentile rank

I can calculate percentile rank from:

• a complete or incomplete data distribution
• descriptions
• a frequency table or a histogram
• a stem-and-leaf graph

I can interpret a percentile rank Example: Calculate the percentile rank of 5 as the number in the set. N smaller = 9 (the first 4 bars' heights = 1+2+4+2)N equal = 1 (the bar corresponds to the value '5' has height of 1)N total = 11 (heights of all bars = 1+2+4+2+1+1=11)R100 = (9 + 1/2) / 11 * 100 = (9 + 0.5) / 11 * 100 = 9.5 / 11 * 100 = 86.36 ~ 87th percentile rank

Find missing value from its percentile

I can calculate a value from its percentile rank Example: Reverse the percentile rank calculation.

1. 88 percentile divided by 100 = 0.88
2. 0.88 times the total number of values, 0.88x20=17.6
3. Assuming N= is just one. So N=/2 = 0.5. Plus 0.5 becomes minus 0.5 when reversing the calculation17.6 - 0.5 = 17.1 ~ 17
4. There are 17 number less than the value in question.The answer is therefore $35

Scatter plot

• Graphing area should be square-ish
• Each axis (x and y) can use the same or different intervals
• Each axis (x and y) can start at 0 or not.
• Each axis should be labelled
• The graph should have a title

Regression line

Draw a straight line representing the overall pattern seen in the scatter plot Ignore the outlier(s) - one or more points that are clearly far away from the rest of the data. *Outlier will be VERY OBVIOUS in this course. Example:

Linear equation

Sign & strength

Positive correlations (blue), from strong to weak (top to bottom). Negative correlation (orange), from strong to weak (top to bottom)

Box method

Draw a rectangular box to surround all the data points* *excluding the outlier(s) Then measure the width and length of the box using your rule. Use the formula to estimate the correlation coefficient.

Interpretation

A correlation with a strong correlation coefficient would mean

• the linear regression line is very close to most if not all of the data points
• the relationship between the two variables can be very well modelled using the linear equation
• one variable strongly affect the other variable
• the relationship between the two variables can be predicated accurately

Sign of correlation

• I can create a contingency table (also called a correlation table).
• I can determine the sign of the correlation from a contingency table.

Example of a positive correlation Example of a negative correlation

One variable

Analyses on one variable on a time, including:

• Frequency table, bar graph and histogram
• Stem-and-leaf graph
• Mean, mean deviation and range
• Percentile rank

Two variables

Focusing on how one variable affects the other variable. Usually the first column/row is:

• the independent variable
• x or the horizontal axis on the cartesian graph

And the second column/row is:

• the dependent variable
• y or the vertical axis on the cartesian graph

Statistics

Vocabulary

• Population means the group of individuals or items of interests in a statistical study
• Sample means a part of the population
• Qualitative data are responses that describes feelings etc.
• Quantitative data are numerical values from counting or measuring
  • Quantitative and discrete data are from counting
  • Quantitative and continuous data are from measuring

Contingency table

Example: