Chapter 10.4, Problem 21PFA

a.

To determine

To calculate median of the data.

Answer to Problem 21PFA

Median is 48000

Explanation of Solution

Given information:

Employee salary($)
31,000	48,000	37,000	43,000	52,000
48,000	36,000	56,000	59,000	58,000
34,000	256,000	63,000	45,000	37,000

Formula used:

Median= $\frac{{(n+1)}^{th}}{2}observation$ , where n is total terms.

Calculation:

Sorting values,

31000,34000,36000,37000,37000,43000,45000,48000,48000,52000,56000,58000,59000,63000,256000

Total data=15

For median substituting the values,

  $median={(\frac{15+1}{2})}^{th}ob$

On solving,

  $median=8^{th}ob$

Substituting the value,

  $median=48000$

Hence, Median is 48000

b.

To determine

To find mean of the data

Answer to Problem 21PFA

Mean is 60200

Explanation of Solution

Given information:

Employee salary($)
31,000	48,000	37,000	43,000	52,000
48,000	36,000	56,000	59,000	58,000
34,000	256,000	63,000	45,000	37,000

Formula used:

Mean= $\frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}$

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms

Calculation:

For Mean substituting the values,

  $\frac{31000+34000+36000+37000+37000+43000+45000+48000+48000+52000+56000+58000+59000+63000+256000}{15}$

So,

  $=\frac{903000}{15}$

On solving,

  $=60200$

Hence, Mean is 60200

c.

To determine

To explain why median is more appropriate than mean

Explanation of Solution

Given information:

Data’s mean and median.

Median divides the whole data in two equal parts allow the data to be examined or read

While mean is only an arithmetical average of the data. Hence, median is a more appropriate than mean.