Measures of Variation

Statistical Measures Part 2

By KAZU HOSHINO

Measures of Variation

definition

Measures of variation describe the spread of a distribution. They define how spread out the values are in a data set. They include: range, median (because it helps to find Q1 and Q3), Q1, Q3, and IQR

Some text here about the topic of discussion

Multiple Choice

Which of the following is NOT a measure of variation?

• mean

• range

• Q1

• IQR

Multiple Choice

The range measures the width between the highest and lowest values in a data set. Which of these is the range for the data set shown below:

2, 5, 16, 18, 19, 100

• 102

• 100

• 98

• 50

Multiple Select

Q1, or Quartile 1, is the value that identifies the middle of the lower half. Q3, or Quartile 3, is the value that identifies the middle of the upper half. Which of the following is true based on the image shown? Choose ALL that apply.

• 25% or 1/4 of the values are below Q1.

• 25% or 1/4 of the values are between Q1 and the median.

• 25% or 1/4 of the values are between the median and Q3.

• 25% of 1/4 of the values are above Q3.

Multiple Select

Which of the following is true based on the data set shown? Choose ALL that apply.

• The median is 5.

• Q1 is 4.

• Q3 is 6.5

Multiple Choice

IQR, or Interquartile Range, is the range between Q1 and Q3. It measures the spread of the middle quartiles. Which of the following describes the appropriate steps for calculating the IQR?

• Q1 + Q3

• Q1 - Q3

• Q3 - Q1

• Q3 ÷ Q1

Multiple Choice

Q1 and/or Q3 is a decimal number (ex. 7.5). This is true....

• All of the time

• Some of the time

• Never

Multiple Select

An outlier is a value that is much smaller or much greater than other values in a data set.

An outlier can affect the mean, or average of a set of data by adding in a value that is extremely small or extremely high. Which of the following is true about outliers? Choose ALL that apply.

• Outliers are much smaller or greater than the other values in a set.

• Outliers are always below Q1 or above Q3.

• Outlier greatly affect the mode.

• Outliers greatly affect the median.

Multiple Select

We can identify outliers by setting boundaries.

1. multiply 1.5 x IQR to determine the stretcher.

2. Lower boundary = Q1 - stretcher

3. Upper boundary = Q3 + stretcher

Which of the following is true about outliers? Choose ALL that apply.

• Outliers are lower than the lower boundary

• Outliers are greater than the upper boundary

• There are always outliers in a data set.

• There can be more than one outlier in a data set.

Multiple Select

Mean Absolute Deviation (M.A.D.) is the average distance between each value and the mean of a data set. Which of the following is true about M.A.D.? Choose ALL that apply.

• You must put the numbers in order to find the mean.

• M.A.D. can be negative.

• M.A.D. must be positive

• M.A.D. can be a decimal number.

Multiple Select

Steps for finding the M.A.D.:

1. find the mean or average

2. find the deviations

3. find the mean of the deviations

Use the example shown here. Which of the following statements is true? Choose ALL that apply.

• The M.A.D. is 3.4

• The mean is 3.4

• The M.A.D. is 0.88

• There are five values in this data set.

Multiple Choice

The two players have the same mean and median. Which player has the greater M.A.D.? You should not have to calculate it.

• Terry (top dot plot)

• Chris (bottom dot plot)

• They have the same M.A.D.

Multiple Choice

The two data sets have the same mean and median. Which data set has the greater M.A.D.? You should not have to calculate it.

• Blue dot plot

• Red dot plot

• They have the same M.A.D.

Open Ended

Give one tip for calculating Outliers or M.A.D. accurately.