Question

Benjamin owns a small Internet business. Besides​ himself, he employs nine other people. The salaries earned by the employees are given below in thousands of dollars​ (Benjamin's salary is the​ largest, of​ course). Complete parts​ (a) through​ (d) below. 10​, 30​, 45​, 50​, 50​, 55​, 55​, 55​, 60​, 80

​(a) Determine the​ mean, median, and mode for salary.

The mean salary is -----thousand dollars.

​(Type an integer or a decimal. Do not​ round.)

The median salary is----- thousand dollars.

​(Type an integer or a decimal. Do not​ round.)

Select the correct choice below and fill in any answer boxes in your choice.

A. The mode salary is ----- thousand dollars.

​(b) The business has been​ good! As a​ result, Benjamin has a total of ​$24,500 in bonus pay to distribute to his employees. One option for distributing bonuses is to give each employee​ (including himself) ​$2,450 Add the bonuses under this plan to the original salaries to create a new data set. Recalculate the​ mean, median, and mode. How do they compare to the​ originals?

mean for the new data set--- thousand

median---- thousand

mode ---- thousand

How do the​ mean, median, and mode compare to the​ originals?

A.The mean increased by

​$2 comma 4502,450​,

but the median and the mode did not change.

B.

All three measures increased by​ 10%.

C.All three measures increased by

​$2 comma 4502,450.

D.

The​ mean, median, and mode did not change.

Answer 1

​(a) Determine the​ mean, median, and mode for salary.

	x
1	10,000
2	30,000
3	45,000
4	50,000
5	50,000
6	55,000
7	55,000
8	55,000
9	60,000
10	80,000
Total	490,000

Mean = Sum / n

= 490,000 / 10

= 49,000

The mean salary is 49 thousand dollars.

Median = (N + 1) /2 th value

= 5.5th value

= 5th + 0.5(6th - 5th)

= 50 + 0.5 *(55 - 50)

= 52.5

The median salary is 52.5 thousand dollars.

Mode is the value with the highest frequency. Here since 55 is repeated the most so

The mode salary is 55 thousand dollars.

​(b) The business has been​ good! As a​ result, Benjamin has a total of ​$24,500 in bonus pay to distribute to his employees. One option for distributing bonuses is to give each employee​ (including himself) ​$2,450 Add the bonuses under this plan to the original salaries to create a new data set. Recalculate the​ mean, median, and mode. How do they compare to the​ originals?

	New X
1	12,450
2	32,450
3	47,450
4	52,450
5	52,450
6	57,450
7	57,450
8	57,450
9	62,450
10	82,450
Total	514,500

Mean = 514500 / 10

= 51450

mean for the new data set 51.45 thousand   (49+2.45)

we notice that if the same amount is added to all the values then there is a same absolute increase in the mean as well. Here we are using the entire data set.

Median = 5.5th value

= 54,950

median 54.95 thousand   (52.5 + 2.45)

Here unlike mean we use only 1 or 2 values. So if the increase is same for all the rank will remain the same. Therefore the new median will increase too by same amount in absolute terms.

The value of 57450 is repeated highest.

mode 57.45 thousand (55 + 2.45)

Like median mode is only affected by one value if the number of frequency changes then it will change. Since same amount is added there is no change the frequencies. So it has same absolute change.

How do the​ mean, median, and mode compare to the​ originals?

C.All three measures increased by $2,450.

Please give it a thumps up if the solution helped you.