Mad Variance and Standard Deviation

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

What is the last step to solving for the Mean Absolute Deviation?

• Find the mean of the new set of numbers

• Find the mean of the given data set

• Subtract the mean from each original data point

Which of the following is true concerning the mean absolute deviation of a set of data?

• It describes the variation of the data values around the median.

• It describes the absolute value of the mean.

• It describes the average distance between each data value and the mean.

• It describes the variation of the data values around the mode.

What is the first step when calculating the Mean Absolute Deviation?

• Find the distance each value is from the mean

• Find the mean of the distances

• Find the mean of the data

What does M.A.D stand for?

• Mean as Dirt

• Mean Average Deviation

• Crazy

• Mean Absolute Deviation

If the standard deviation of a data set is 4, what is the variance?

• 2

• 16

• 4

• 8

Answer explanation

The variance is the square of the standard deviation. Therefore, if the standard deviation is 4, then the variance is $4^2=16$

Ervin bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the standard deviation of Ervin's scores?

• 511.33

• 22.61

• 438.48

• 20.94

Answer explanation

Use your calculator or calculator application.
1. Hit STAT then ENTER
2. Enter all data values in L1
3. Hit STAT again
4. Arrow over to CALC
5. Choose #1:1 Var Stats, hit ENTER
6. Scroll down to find the standard deviation ( $\sigma$ )

Which of the following is a measure of dispersion?

• mean

• median

• mode

• standard deviation

Answer explanation

Standard deviation is a measure of dispersion, or a measure of the average distance of each value from the mean.

What is the standard deviation for the data given:

{12, 13, 29, 18, 61, 35, 21}

• 251.86

• 15.87

• 27

• 189

Answer explanation

Use your calculator or calculator application.

1. Hit STAT then ENTER

2. Enter all data values in L1

3. Hit STAT again

4. Arrow over to CALC

5. Choose #1:1 Var Stats, hit ENTER

6. Scroll down to find the standard deviation (σ)

Which set of data probably has the points closest to the 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

Answer explanation

A lower standard deviation indicates that the values are closer together. Set 3 has the lowest standard deviation.