Chapter 11.1, Problem 35E

To determine

To find the values of Mean, Median, Mode, Range and Standard deviation when multiplied by 3 and increased by 8.

Answer to Problem 35E

Mean: $89$

Median: $104$

Mode: $62$

Range: $123$

Standard deviation: $81$

Explanation of Solution

Given information: Mean: $27$ , Median: $32$ , Mode: $18$ , Range: $41$ and Standard deviation: $9$

Calculation:

• As a general rule, the median, mean, and mode will be changed by adding a constant to each value. However, the range, standard deviation and variance will remain the same.
• 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 3 and increased by 8.

• Mean

Mean: $27$

Now,

When multiplied by 3 and increased by 8.

So,

Mean: $\left(3\times 27\right)+8$

Now,

Mean: $81+8$

Hence,

Mean: $89$

• Median

Median: $32$

Now,

When multiplied by 3 and increased by 8.

So,

Median: $\left(3\times 32\right)+8$

Now,

Median: $96+8$

Hence,

Median: $104$

• Mode

Mode : $18$

Now,

When multiplied by 3 and increased by 8.

So,

Mode: $\left(3\times 18\right)+8$

Now,

Mode: $54+8$

Hence,

Mode: $62$

• Range

Range: $41$

Now,

When multiplied by 3 and increased by 8.

So,

Range: $41\times 3$

Hence,

Range: $123$

• Standard Deviation

Standard deviation: $9$

Now,

When multiplied by 3 and increased by 8.

So,

Standard deviation: $9\times {\left(3\right)}^2$

Hence,

Standard deviation: $81$