Assume that researchers are interested in determining whether different forms of
ID: 3200371 • Letter: A
Question
Assume that researchers are interested in determining whether different forms of TV watching are equivalent. To this end, they measured the thoughts generated by eight-year-olds while watching ten randomly picked television shows: five from the Discovery Channel and five reality shows. For both types of shows, the number of thoughts was tabulated. The complexity of each thought was rated by independent judges, and the score for the most complex thought was recorded. The data are presented in Table 5.1. For each variable, find the mean, median, mode, range, variance, standard deviation, skewness, and kurtosis. What do these statistics tell us about the thoughts of eight-year-olds while watching these two different types of shows?
Case Reality TV Thoughts per min. Discovery Channel Thoughts per min. Reality TV Thought Complexity Discovery Channel Thought Complexity 1 4 1 0 3 2 5 1 1 5 3 6 1 2 6 4 6 2 2 6 5 7 2 2 7 6 7 2 2 7 7 7 2 2 7 8 8 3 2 7 9 8 3 2 7 10 8 3 2 7 11 8 3 2 7 12 8 3 2 7 13 8 3 2 7 14 9 4 2 7 15 9 4 2 7 16 9 4 2 7 17 10 4 2 8 18 10 5 2 8 19 11 5 3 9 20 12 6 4 9Explanation / Answer
Answer:
Assume that researchers are interested in determining whether different forms of TV watching are equivalent. To this end, they measured the thoughts generated by eight-year-olds while watching ten randomly picked television shows: five from the Discovery Channel and five reality shows. For both types of shows, the number of thoughts was tabulated. The complexity of each thought was rated by independent judges, and the score for the most complex thought was recorded. The data are presented in Table 5.1. For each variable, find the mean, median, mode, range, variance, standard deviation, skewness, and kurtosis. What do these statistics tell us about the thoughts of eight-year-olds while watching these two different types of shows?
Descriptive statistics
Reality TV Thoughts
per min.
Discovery Channel
Thoughts per min.
Reality TV
Thought Complexity
Discovery Channel
Thought Complexity
n
20
20
20
20
mean
8.00
3.05
2.00
6.90
sample standard deviation
1.95
1.39
0.73
1.29
sample variance
3.79
1.94
0.53
1.67
minimum
4
1
0
3
maximum
12
6
4
9
range
8
5
4
6
skewness
0.00
0.29
0.00
-1.25
kurtosis
0.20
-0.37
5.33
3.88
coefficient of variation (CV)
24.33%
45.72%
36.27%
18.75%
1st quartile
7.00
2.00
2.00
7.00
median
8.00
3.00
2.00
7.00
3rd quartile
9.00
4.00
2.00
7.00
interquartile range
2.00
2.00
0.00
0.00
mode
8.00
3.00
2.00
7.00
Average value of Reality TV Thoughts per min is more (8.0) compared to Discovery Channel Thoughts per min.(3.05). The average value of Reality TV Thought Complexity (2) is smaller compared to Discovery Channel Thought Complexity(6.90).
The variation in Reality TV Thoughts per min is more (1.95) compared to Discovery Channel Thoughts per min.(1.39). The variation in Reality TV Thought Complexity is (0.73) smaller compared to Discovery Channel Thought Complexity(1.29).
Descriptive statistics
Reality TV Thoughts
per min.
Discovery Channel
Thoughts per min.
Reality TV
Thought Complexity
Discovery Channel
Thought Complexity
n
20
20
20
20
mean
8.00
3.05
2.00
6.90
sample standard deviation
1.95
1.39
0.73
1.29
sample variance
3.79
1.94
0.53
1.67
minimum
4
1
0
3
maximum
12
6
4
9
range
8
5
4
6
skewness
0.00
0.29
0.00
-1.25
kurtosis
0.20
-0.37
5.33
3.88
coefficient of variation (CV)
24.33%
45.72%
36.27%
18.75%
1st quartile
7.00
2.00
2.00
7.00
median
8.00
3.00
2.00
7.00
3rd quartile
9.00
4.00
2.00
7.00
interquartile range
2.00
2.00
0.00
0.00
mode
8.00
3.00
2.00
7.00