Question

Data Set A has a mean of 67 and Data Set B has a mean of 92. The MAD of each data set is 12. Express the difference in the measures of center as a multiple of the measure of variation. Round your answer to the nearest tenth.

Answer 1

Data Set A has a mean of 67  

Data Set B has a mean of 92.

The MAD of each data set is 12

Express the difference in the measures of center as a multiple of the measure of variation.

We find the difference of mean and divide by MAD

$\frac{Data \ set \ B - Data \ set \ A}{MAD}$

$\frac{92 - 67}{12}$ = 2.0833

So, the difference in the means is about 2.1 times the MAD

Answer 2

2.1 is difference in the measures of center as a multiple of the measure of variation.

It is given that the data set A has mean of 67 and data set B has a mean of 92.

It is required to find the difference in the measures of center as a multiple of the measure of variation if MAD of each data set is 12.

What is mean absolute deviation?

It is defined as the measure to show the variation in data set in other words between the mean and every data value the distance known as the MAD.

We have mean value of data set A = 67

Mean value of data set B = 92

The MAD = 12

We can use the below relation to find the difference in means:

$\rm = \frac{Data \ set \ B- Data\ set\ A}{MAD}$

$= \frac{92-67}{12}$

$=\frac{25}{12}$

= 2.0833 ≈ 2.1 (round to nearest tenth)

Thus, 2.1 is difference in the measures of center as a multiple of the measure of variation.

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