Chapter 6, Problem 2P

Solution

To Explain: The statistic that does not change when non zero constant is added to each value of data.

Range does not change.

Given information: Non zero constant added to each value in a data.

Calculation:

Let consider an example to understand this concept.

Consider the data set:

  $3,3,7,9,13$

Now, calculate the values of mean, median, mode and range.

Mean can be calculated as sum all the numbers and divide them with total numbers. Mode is the most repeated number in the set.

Mean: $\frac{3+3+7+9+13}{5}=7$

Median: $7$

Mode: $3$

Range: $13-3=10$

Now, add $6$ to the all numbers then, again find:

Mean: $\frac{9+9+13+15+19}{5}=13$

Median: $13$

Mode: $9$

Range: $19-9=10$

Hence, range is the one which does not change when a non-zero value is added to each data.