Ch3 Test Questions & Answers Central Tendency And Dispersion - Statistics for Criminology 1e | Test Bank Cooper by Jonathon A. Cooper. DOCX document preview.
Chapter 3: Central Tendency and Dispersion
- Name the three measures of central tendency and indicate their purpose. Also, determine the level of measurement that is required for the individual measure.
- In what circumstances would you chose the median over the mean? (Assume the calculation of either is possible.)
- The following table represents the number of individuals within a federal prison categorized by race. Which measures of central tendency can you compute? Compute/determine all that are possible.
Race/ethnicity | f |
Caucasian | 215 |
African American | 455 |
Native American | 120 |
Hispanic/Latino | 222 |
Asian | 95 |
Other | 26 |
- The following represents the results of a survey conducted with 25 high school students indicating the number of times (f) the individual student has skipped class within the past academic year. Which measures of central tendency can you compute? Compute/determine all that are possible. Also indicate whether the distribution is positively or negatively skewed.
No. skipped | f |
0 | 3 |
1 | 8 |
2 | 1 |
3 | 0 |
4 | 3 |
5 | 0 |
6 | 4 |
7 | 2 |
8 | 0 |
9 | 0 |
10 | 2 |
11 | 1 |
12 | 1 |
- The following table displays how often graduate students at your school (random sample of 50) have used marijuana in their life. Which measures of central tendency can you compute? Compute/determine all that are possible.
Code | Use | No. |
0 | Never | 7 |
1 | 1–5 | 17 |
2 | 6–10 | 4 |
3 | 11–15 | 6 |
4 | 16–20 | 8 |
5 | 21–25 | 5 |
6 | 26+ | 3 |
Total | 50 | |
- Calculate the mode, median, and mean for the following distribution of scores. Also indicate whether the distribution is positively or negatively skewed.
5 | 6 | 2 |
6 | 3 | 3 |
4 | 1 | 9 |
3 | 2 | 10 |
1 | 9 | 3 |
2 | 8 | 6 |
7 | 5 | 8 |
8 | 6 | 7 |
9 | 6 | 5 |
6 | 9 | 5 |
- Calculate the mode, median, and mean for the following distribution of scores. Also indicate whether the distribution is positively or negatively skewed.
21 | 23 |
23 | 15 |
15 | 7 |
2 | 6 |
3 | 23 |
9 | 15 |
21 | 6 |
19 | 8 |
23 | 15 |
8 | 17 |
- Indicate the three main measures of dispersion (which were discussed in this chapter) and briefly describe their purpose.
- What is the reason for the denominator in the formula of (sample) variance and (sample) standard deviation to be n – 1 and not simply n?
- Let’s go back to the distribution we utilized in problem 4 (how often students skipped class in the past 12 months). Compute the range, variance, and standard deviation.
No. skipped | f |
0 | 3 |
1 | 8 |
2 | 1 |
3 | 0 |
4 | 3 |
5 | 0 |
6 | 4 |
7 | 2 |
8 | 0 |
9 | 0 |
10 | 2 |
11 | 1 |
12 | 1 |
- Let’s take the distribution provided in problem 6. Compute the range, variance, and standard deviation.
5 | 6 | 2 |
6 | 3 | 3 |
4 | 1 | 9 |
3 | 2 | 10 |
1 | 9 | 3 |
2 | 8 | 6 |
7 | 5 | 8 |
8 | 6 | 7 |
9 | 6 | 5 |
6 | 9 | 5 |
- The following is a distribution representing the number of prior convictions of 26 inmates of a local county jail. Compute the range, variance, and standard deviation.
5 | 0 |
0 | 1 |
8 | 13 |
1 | 8 |
3 | 9 |
0 | 7 |
4 | 6 |
1 | 6 |
12 | 7 |
0 | 2 |
2 | 0 |
3 | 4 |
11 | 9 |
x | f |
1 | 2 |
2 | 3 |
3 | 4 |
4 | 1 |
5 | 4 |
6 | 6 |
7 | 2 |
8 | 3 |
9 | 4 |
10 | 1 |
x | f |
2 | 1 |
3 | 1 |
6 | 2 |
7 | 1 |
8 | 2 |
9 | 1 |
15 | 4 |
17 | 1 |
19 | 1 |
21 | 2 |
23 | 4 |
Score | Mean | x – | (x – )2 |
0 | 4.12 | –4.12 | 16.9744 |
0 | 4.12 | –4.12 | 16.9744 |
0 | 4.12 | –4.12 | 16.9744 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
1 | 4.12 | –3.12 | 9.7344 |
2 | 4.12 | –2.12 | 4.4944 |
4 | 4.12 | –0.12 | 0.0144 |
4 | 4.12 | –0.12 | 0.0144 |
4 | 4.12 | –0.12 | 0.0144 |
6 | 4.12 | 1.88 | 3.5344 |
6 | 4.12 | 1.88 | 3.5344 |
6 | 4.12 | 1.88 | 3.5344 |
6 | 4.12 | 1.88 | 3.5344 |
7 | 4.12 | 2.88 | 8.2944 |
7 | 4.12 | 2.88 | 8.2944 |
10 | 4.12 | 5.88 | 34.5744 |
10 | 4.12 | 5.88 | 34.5744 |
11 | 4.12 | 6.88 | 47.3344 |
12 | 4.12 | 7.88 | 62.0944 |
∑= 103 | |||
= 4.12 | ss = 342.64 |
Score | Mean | x – | (x – )2 |
5 | 5.47 | –0.47 | 0.2209 |
6 | 5.47 | 0.53 | 0.2809 |
4 | 5.47 | –1.47 | 2.1609 |
3 | 5.47 | –2.47 | 6.1009 |
1 | 5.47 | –4.47 | 19.9809 |
2 | 5.47 | –3.47 | 12.0409 |
7 | 5.47 | 1.53 | 2.3409 |
8 | 5.47 | 2.53 | 6.4009 |
9 | 5.47 | 3.53 | 12.4609 |
6 | 5.47 | 0.53 | 0.2809 |
6 | 5.47 | 0.53 | 0.2809 |
3 | 5.47 | –2.47 | 6.1009 |
1 | 5.47 | –4.47 | 19.9809 |
2 | 5.47 | –3.47 | 12.0409 |
9 | 5.47 | 3.53 | 12.4609 |
8 | 5.47 | 2.53 | 6.4009 |
5 | 5.47 | –0.47 | 0.2209 |
6 | 5.47 | 0.53 | 0.2809 |
6 | 5.47 | 0.53 | 0.2809 |
9 | 5.47 | 3.53 | 12.4609 |
2 | 5.47 | –3.47 | 12.0409 |
3 | 5.47 | –2.47 | 6.1009 |
9 | 5.47 | 3.53 | 12.4609 |
10 | 5.47 | 4.53 | 20.5209 |
3 | 5.47 | –2.47 | 6.1009 |
6 | 5.47 | 0.53 | 0.2809 |
8 | 5.47 | 2.53 | 6.4009 |
7 | 5.47 | 1.53 | 2.3409 |
5 | 5.47 | –0.47 | 0.2209 |
5 | 5.47 | –0.47 | 0.2209 |
∑ = 164 | ss = 199.467 | ||
= 4.12 |
Score | Mean | x – | (x – )2 |
5 | 4.69 | 0.31 | 0.0961 |
0 | 4.69 | –4.69 | 21.9961 |
8 | 4.69 | 3.31 | 10.9561 |
1 | 4.69 | –3.69 | 13.6161 |
3 | 4.69 | –1.69 | 2.8561 |
0 | 4.69 | –4.69 | 21.9961 |
4 | 4.69 | –0.69 | 0.4761 |
1 | 4.69 | –3.69 | 13.6161 |
12 | 4.69 | 7.31 | 53.4361 |
0 | 4.69 | –4.69 | 21.9961 |
2 | 4.69 | –2.69 | 7.2361 |
0 | 4.69 | –4.69 | 21.9961 |
1 | 4.69 | –3.69 | 13.6161 |
13 | 4.69 | 8.31 | 69.0561 |
8 | 4.69 | 3.31 | 10.9561 |
9 | 4.69 | 4.31 | 18.5761 |
7 | 4.69 | 2.31 | 5.3361 |
6 | 4.69 | 1.31 | 1.7161 |
6 | 4.69 | 1.31 | 1.7161 |
7 | 4.69 | 2.31 | 5.3361 |
2 | 4.69 | –2.69 | 7.2361 |
0 | 4.69 | –4.69 | 21.9961 |
3 | 4.69 | –1.69 | 2.8561 |
11 | 4.69 | 6.31 | 39.8161 |
4 | 4.69 | –0.69 | 0.4761 |
9 | 4.69 | 4.31 | 18.5761 |
∑ = 122 | ss = 407.5386 | ||
= 4.69 |
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Statistics for Criminology 1e | Test Bank Cooper
By Jonathon A. Cooper