Chapter 13.2, Problem 66E

a.

To determine

The mean, median and mode of the measurements.

Answer to Problem 66E

All the measures of the central tendency are increased by $6$ .

Explanation of Solution

Given Information: Given data set is: $5,12,7,14,8,9,7,12$

Calculation:

Mean, median and modes of the given data set are $9.25;8.5;7,12$ respectively.

Adding $6$ to this data set, the new data set is:

  $11,13,13,14,15,18,18,20$

Mean $=\frac{11+13+13+14+15+18+18+20}{8}=15.25$

Median $=\frac{14+15}{2}=14.5$

Modes $=13,18$

Thus, all the measures of the central tendency are increased by $6$ .

b.

To determine

The change in measures of central tendency of a data set when a constant $k$ is added to each data value.

Answer to Problem 66E

All the measures of the central tendency are increased by $k$ .

Explanation of Solution

Given Information: A conjecture on the measures of central tendency of a data set is to be made.

From part (a), it can be generalized that after adding a constant $k$ to each data value of a data set, all the measures of the central tendency are increased by $k$ .