Question

Discuss why the median is a more stable measure of central tendency than the mean. Provide an original example in your discussion. (2 pts)

3. Why do we generally consider the mean to be a more precise measure of central tendency than either the median or the mode? (1 pt)

4. Discuss why a mean should not be used with ordinal level variables. Justify your answer. (1 pt)

5. For each of the following, indicate the measure of central tendency that would be most appropriate, and indicate why. (6 pts)

a. An income distribution in which 97% of the cases are in a range of $20,000 to $90,000 and a few cases are between 0 and $5,000.

b. Data reporting the religious preferences of 100 social work students.

c. A grouped frequency distribution of the variable age that has an open-ended interval of over 65 years

6. 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

2. Since the median is less affected by outliers and skewed data than the mean, so median is a more stable measure of central tendency than the mean.

For example:

For example, consider the wages of staff at a factory below:

Staff	1	2	3	4	5	6	7	8	9	10
	15k	18k	16k	14k	15k	15k	12k	17k	90k	95k

The mean salary=(15+18+16+14+15+15+12+17+90+95)/10=$30.7k. However, this mean value might not reflect the typical salary of a worker, since most workers have salaries in the $12k to 18k range. So the mean is affected by the two large salaries. Therefore, in this situation, we use median than mean.

3. Since mean includes all of the data in the calculations so mean is a more precise measure of central tendency than either the median or the mode.

4. Mean should not be used with ordinal level variable since its value depends on conventions on coding.

5.

a. An income distribution in which 97% of the cases are in a range of $20,000 to $90,000 and a few cases are between 0 and $5,000: Median

b. Data reporting the religious preferences of 100 social work students: Mode

c. A grouped frequency distribution of the variable age that has an open-ended interval of over 65 years: Median