Measure of Center and Variability in a Data Set

Median and IQR

Median - the middle value in an ordered data set

●Roughly 50% of the data is below and above the median

●Measures the typical value for data in a skewed distribution

●NOT influenced by all data values

Interquartile Range (IQR) - the middle 50% of the data in a distribution

●Found by subtracting the 1st quartile (Q1) from the 3rd quartile (Q3)

●Measures the variability of a sample with a skewed distribution

Multiple Select

Select the (2) measures of CENTER.

• Mean

• Median

• IQR

• Standard Deviation

Multiple Select

Select the (2) measures of VARIABILITY.

• Mean

• Median

• IQR

• Standard Deviation

Appropriate Measures of Center and

Variation

• The shape of the distribution determines which measure of center
  and variability are best.

• Use the mean and standard deviation for symmetrical distributions.

• Use the median and IQR for skewed distributions or distributions that have outliers.

Multiple Choice

If there is an Outlier in the set which measure of CENTER would you use?

• Mean

• Median

• IQR

• Standard Deviation

Comparing Measures of Center

●

In a symmetric distribution, the mean and the median are
approximately the same.

●

In a right skewed distribution the mean tends to be greater than the
median.

●

In a left skewed distribution the mean tends to be less than the
median.

Multiple Choice

If there is an Outlier in the set which measure of VARIABILITY would you use?

• Mean

• Median

• IQR

• Standard Deviation

Multiple Choice

If there is NOT an Outlier in the set which measure of VARIABILITY would you use?

• Mean

• Median

• IQR

• Standard Deviation

Multiple Choice

If there is NOT an Outlier in the set which measure of CENTER would you use?

• Mean

• Median

• IQR

• Standard Deviation

Multiple Select

Which measurements would represent the BEST measures of center & variability for the data set shown?

26, 29, 24, 33, 31, 43, 17, 84, 23, 27, 29

• Mean

• Median

• IQR

• Standard Deviation

Multiple Select

Which measurements would represent the BEST measures of center & variability for the data set shown?

8, 7, 6, 5, 4, 4, 3, 2, 9, 7

• Mean

• Median

• IQR

• Standard Deviation

Multiple Select

Study the graph and determine one measure of center and one measure of variability that would best describe the data. (hint: are there outliers?)

• Standard Deviation

• Median

• Mean

• IQR

Multiple Choice

Describe the shape of the distribution.
 

• Skewed Left
• Skewed Right
• Uniform
• Normal

Multiple Choice

Describe the shape of the distribution.
 

• Skewed Left
• Skewed Right
• Uniform
• Normal

Multiple Choice

Describe the shape of the distribution.
 

• Skewed Left
• Skewed Right
• Symmetric
• Uniform

Multiple Choice

Type of Data arrangement

• Symmetrical

• Hairline

• Skewed Right

• Skewed Left

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT

• SKEWED RIGHT

• SYMMETRICAL

Multiple Choice

A data value that is much higher or much lower than the other values in a data set.

• outlier
• inlier
• immalier
• sublier

Drag and Drop

This distribution is ​

Placeholder

so we should use the ​

Placeholder

as a measure of center and the ​

Placeholder

as a measure of variability.

Drag these tiles and drop them in the correct blank above

right skewed

median

IQR

fairly symmetric

left skewed

mean

standard deviation

range

mode

Drag and Drop

This distribution is ​

Placeholder

so we should use the ​

Placeholder

as a measure of center and the ​

Placeholder

as a measure of variability.

Drag these tiles and drop them in the correct blank above

fairly symmetric

mean

range

left skewed

mode

median

IQR

right skewed