Assignment #3
1. For each of the following situations, identify the measure of central tendency (mean, median, or
mode) that would provide the best description of the “average” score. Explain your reasoning.
a. A researcher asks each individual in a sample of 50 adults to name his/her favorite season
(summer, fall, winter, or spring). (1 point)
Using mode as measure of central tendency would provide best description of the average score
because the given situation is on a nominal scale, so it cannot be calculated using mean or
median.
b. An insurance company would like to determine how long people remain hospitalized after a
routine appendectomy. The data from a large sample indicate that most people are released
after 2 or 3 days, but a few develop infections and stay in the hospital for weeks. (1 point)
The given variable in this situation is on a ratio scale (it has number and the 0 is absolute), and
the data are likely skewed due to a few people who develop infections, so the best measure of
central tendency would be median.
c. A teacher measures scores on a standardized reading test for a sample of children from a
middle-class, suburban elementary school. (1 point)
The reading test scores in this situation is on a ratio scale, so that allows for median and mean
measure of central tendency. In this case, using mean as the measure of central tendency would
provide the best description of the average score because the data are not skewed, so we can
assume that it is normally distributed.
2. A sample of n = 8 scores has a mean of M = 20. If one of the scores is changed from X = 4 to X = 12,
what will be the new value for the sample mean? Show your work. (2 points)
Mean = ∑ X / N, n=8, M=20
20 = ∑ X / 8
∑ X = 160
12-4 = 8  160+8 = 168
New ∑ X = 168
Mean = ∑ X / N = 168/8  M = 21
3. One sample of n=20 has a mean of M=50. A second sample has n=5 scores has a mean of M=10. If the
two samples are combined, what is the mean for the combined sample? Show your work. (2 points)
First sample: n1=20, M1=50,
Mean = ∑ X / N  ∑ X = N(Mean)
∑ X1 = N (Mean) = 20(50) = 1000
Second sample: n2=5, M2=10,
∑ X2 = N(Mean) = 5(10) = 50
Mean of combined sample = (∑ X1 + ∑ X2)/ (n1+n2) = (1000+50)/(20+5) = 1050/25 = 42
4. Showing your work, find the mean, median, and mode for the set of scores in the following frequency
distribution table: (3 points)
X
5
4
3
2
1
f
1
2
3
5
1
Mean = (∑fX) / (∑f) = (5+8+9+10+1)/ (1+2+3+5+1) = 33/12= 2.75
Median =
fX
5
8
9
10
1