Chapter 10.5, Problem 22HP

To determine

To find mean, median, mode, range and deviation

Answer to Problem 22HP

The answer is as follows

Explanation of Solution

Given information: Constant k and a random data set

If we multiply a data set by a constant k where k<0, the given statistics will be multiplied by the k.

Taking an example,

Let’s pretend the data set be 3, 3, 7, 9, 13, and let’s calculate our measures for the set.

Mean: $\frac{\left(3+3+7+9+13\right)}{5}$ =7

Median: 7

Mode: 3

Range: 13-3=10

IQR: 11-3=8

Multiplying data set by constant k<0 i.e. -2.

Let’s multiply the set by 2, making the new set -6, -6, -14, -18, -26. The new measures of central tendency and spread are

Mean: $\frac{-\left(6+6+14+18+26\right)}{5}=-14$

Median: -14

Mode: -6

Range: -26+ 6= -20

IQR: -22+6= -16

Here we can see the data set when changed give k times statistics.

The standard deviation of both the data sets are also changed in a same way, i.e. will be multiplied by k