Chapter 11.1, Problem 28E

To determine

To find the values of Mean, Median, Mode, Range and Standard deviation when multiplied by $0.5$

Answer to Problem 28E

Mean: $160$

Median: $150$

Mode: none

Range: $105$

Standard deviation: $17.65$

Explanation of Solution

Given information: Mean: $320$ , Median: $300$ , Mode:none, Range: $210$ and Standard deviation: $70.6$

Calculation:

Multiplying every value by a constant, however, will multiply the mean, median, mode, range, and standard deviation by that constant, and multiply the variance (which is simply the square of the standard deviation) by the square of that constant.

When multiplied by $0.5$

• Mean

Mean: $320$

Now,

When multiplied by $0.5$

So,

Mean: $320\times 0.5$

Hence,

Mean: $160$

• Median

Median: $300$

Now,

When multiplied by $0.5$

So,

Median: $300\times 0.5$

Hence,

Median: $150$

• Mode

Mode: none

Now,

When multiplied by $0.5$

Hence,

Mode: none

• Range

Range: $210$

Now,

When multiplied by $0.5$

So,

Range: $210\times 0.5$

Hence,

Range: $105$

• Standard deviation

Standard deviation: $70.6$

Now,

When multiplied by $0.5$

So,

Standard deviation: $70.6\times {\left(0.5\right)}^2$

Hence,

Standard deviation: $17.65$