Measures of Spread

Measures of Spread

by Zanier Fuller

​What is it?

​The spread of a set of data tells you about the variability in the sample or population. In other words, this measure tells you how spread out the data are.

​

The spread of data is important because it can help you assess how well other measures like the mean represent the data. For this reason, measures of center are often reported along with measures of spread.

The Measurements

• ​Range

• ​Interquartile Range (IQR)

• ​Mean Absolute Deviation (MAD)

• ​Standard Deviation (SD)

Multiple Choice

A data set can have more than one median?

• True
• False

Multiple Choice

If a number is added to the set that is near the mean, how does this affect standard deviation?

• increase
• decrease
• stay the same
• both increase and decrease

Multiple Choice

If a number is added to the set that is in the middle of the data, how does this affect the range?

• increase
• decrease
• stay the same
• both increase and decrease

Multiple Choice

Which of the following is a measure of variability?

• mean
• median
• mode
• standard deviation

Multiple Choice

• Kim's scores are more consistent.
• Caleb's scores are more consistent.
• Both scores have the same consistency!
• Not enough information is provided.

Multiple Choice

Quartiles are values that divide a data set into four equal parts.

• True
• False

Multiple Choice

1-  The first quartile (Q 1) is the median of the lower half of the set.
2-  The second quartile (Q 2) is the median of the whole set .
3-  The third quartile (Q 3) is the median of the upper half of the set.

• All three statements are true.
• Only the 1st statement is true.
• Only the 2nd and the 3rd statements are true.
• Only the 3rd statement is true.

Multiple Choice

The interquartile range (IQR) of a data set is the difference between the third and first quartiles. It represents the range of the middle half of the data.

• True
• False

Multiple Choice

Standard Deviation is a measure of spread, which represents the average of the distance between individual data values and the mean.

• True
• False

Multiple Choice

Given the data: 136, 150, 119, 150, 125, 143.
Find the range. 

• Range = 136 - 125 = 21.
• Range = 150 - 125 = 75.
• Range = 150 - 125 = 25.
• Range = 150 - 119 = 31

Multiple Choice

Given the data: 136, 150, 119, 150, 125, 143.
Find the interquartile range (IQR)

•  IQR = 150 - 119 = 31
•  IQR = 150 - 125 = 25.
• IQR = 150 - 125 = 75.
•  IQR = 150 - 119 = 31.

Multiple Choice

• Mode
• Median
• Mean
• IQR

Multiple Choice

What is the range?

• average
• biggest-smallest
• the middle #
• # happening the most

Multiple Choice

Find the lower quartile (Q1) of the following set of scores 6, 7, 8, 9, 11, 13, 15

• 13
• 7

• 9
• 6

Multiple Choice

All of the below sets have the same mean.
Set 1-Standard Deviation=3.1
Set 2-Standard Deviation=4.9
Set 3-Standard Deviation=1.7
Set 4-Standard Deviation=3.2
Which set of data probably has the points closest to the mean?

• 1
• 2
• 3
• 4

Multiple Select

Which statements are true? Check all.

• The IQR tells us how spread out the "core" of the data is.

• The range is greatly influenced by outliers.

• The IQR is greatly influenced by outliers.

• The range and IQR each only give us info about 2 data values, not the entire set of data.

Multiple Choice

What is the deviation from the mean for the Astros?

• 0

• 5

• -3

• 3

Multiple Choice

A teacher looks at a set of test scores from her statistics class. If the test scores have a large variance, what does that tell you about the scores?

• The average score was high.

• The average score was low.

• The scores were very spread out.

• The scores were all close to the mean score.

Multiple Choice

Which statistic measures how spread out the data values are in a data set?

• mean

• mode

• maximum value

• standard deviation

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

Describe the shape of the graph.

• Symmetrical

• Skewed

• Uniform

Multiple Choice

How would you describe this data?

• Skewed Left

• Skewed Right

• Symmetrical

• A total amount

Multiple Choice

What is the shape of the distribution?

• Skewed Left 
• Skewed Right
• Symmetric
• Bimodal

Multiple Choice

How would you describe this distribution?

• Left skewed
• Uniform
• Right Skewed
• Symmetrical

Multiple Choice

True or false, the data is skewed.

• True

• False

Multiple Choice

What is the shape of the data for Lucy's Steakhouse?

• Symmetrical
• Skewed Left
• Skewed Right

Multiple Choice

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

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

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

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

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

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM 
• SYMMETRICAL

Multiple Choice

What is the shape of the distribution?

• Skewed Left

• Skewed Right

• Symmetric

• Bimodal

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right

Multiple Choice

What is the shape of the Data Set?

• Skewed Left

• Symmetrical

• Skewed Right