Question

The measures of central tendency have been reported for three different social service agencies for the variable number of years employed in the agency as follows:

Agency	Mode	Median	Mean
A	16	17	16
B	4	7	10
C	1	3	6

Use the measures of central tendency to describe and compare the staff of the three agencies. (5 pts)

7. Fifteen students were registered in Section 1 and 15 students were registered in Section 2 of a research course. They took the same midterm exam, and their exam scores were distributed as follows:

Section 1: 89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94

Section 2: 77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98

a. Calculate the mode, median, mean, range, variance, and standard deviation for both sections. Include your SPSS output below. (10 pts)

b. Which section did better overall on the exam? Fully justify your answer using the concepts in W&G Chapter 3. (3 pt

Answer 1

SOLUTION 1) VARIABLE: Number of years employed in the agency.

FOR AGENCY A: MEAN= 16 YEARS

MEDIAN=17 YEARS

MODE: 16 YEARS

An employee on average work for 16 years in AGENCY A

Median is greater than mean and mode so the distribution is somewhat negatively skewed.

FOR AGENCY B: MEAN= 10 YEARS

MEDIAN= 7 YEARS

MODE= 4 YEARS

An employee on average work for 10 years in AGENCY B

Median is smaller than mean so the distribution is positively skewed.

FOR AGENCY C: MEAN= 6 YEARS

MEDIAN= 3 YEARS

MODE= 1 YEARS

An employee on average work for 6 years in AGENCY C

Median is smaller than mean so the distribution is positively skewed.

Also if we compare means then we will find that workers worked very less for AGENCY C.

7a) SPSS OUTPUT

SECTION A: MEAN= 73.8

MEDIAN= 78

MODE=45

MEDIAN IS GREATER THAN MEAN . IT IS NEGATIVELY SKEWED.

SECTION B: MEAN= 76.4

MEDIAN=77

MODE= 77

MEAN , MEDIAN AND MODE ARE EQUAL THEREFORE THE DATA IS NORMALLY DISTRIBUTED.

VARIABILITY OF SCORES IS HIGHER IN SECTION A AS COMPARED TO SECTION B

b) SECTION B DID BETTER IN EXAM AS COMPARED TO SECTION A.

Explanation: MEAN SCORE FOR B IS GREATER THAN MEAN SCORE FOR SECTION A.