Center of Variation

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
• Skewed

• 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