Chapter 11.1, Problem 27E

To determine

To find the values of Mean, Median, Mode, Range and Standard deviation when increased by 14.

Answer to Problem 27E

Mean: $76$

Median: $69$

Mode: $63$

Range: $46$

Standard deviation: $15.5$

Explanation of Solution

Given information: Mean: $62$ , Median: $55$ , Mode: $49$ , Range: $46$ and Standard deviation: $15.5$

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.

When increased by $14$ .

• Mean

Mean: $62$

Now,

When increased by $14$ .

So,

Mean: $62+14$

Hence,

Mean: $76$

• Median

Median: $55$

Now,

When increased by $14$ .

So,

Median: $55+14$

Hence,

Median: $69$

• Mode

Mode: $49$

Now,

When increased by $14$ .

So,

Mode: $49+14$

Hence,

Mode: $63$

• Range

Range: $46$

Now,

When increased by $14$ .

So,

Range: $\left(Highest+14\right)-\left(Lowest+14\right)$

Hence,

Range: $46$

• Standard deviation

Standard deviation: $15.5$

Now,

When increased by $14$ .

Hence,

Standard deviation: $15.5$