In recent years, there has been a great deal of interest in the ads that appear during a game. These ads vary in length with most lasting 30 seconds or 60 seconds. The accompanying table contains the ad length and ad scores from a recent game. LOADING... Click the icon to view the data. For the 30-second ads and the 60-second ads separately: a. Compute the mean, median, and mode. b. Compute the variance, standard deviation, range, and coefficient of variation. c. Based on the mean and median, are the data skewed? If so, how? d. Based on the results of (a) through (c), what conclusions can you reach about the scores of 30- and 60-second ads? a. Compute the mean, median, and mode. The mean for 60-second ads is 5.15.1. (Type an integer or decimal rounded to two decimal places as needed.) The mean for 30-second ads is 4.94.9. (Type an integer or decimal rounded to two decimal places as needed.) The median for 60-second ads is nothing. (Type an integer or decimal rounded to two decimal places as needed.) Brand Advertised Time of Ad (sec.) Score Company 1 60 6.95 Company 2 30 6.60 Company 3 30 6.56 Company 4 30 6.46 Company 5 30 6.29 Company 6 30 6.14 Company 7 60 6.12 Company 8 60 6.04 Company 9 60 6.06 Company 10 30 5.90 Company 11 60 5.73 Company 12 60 5.62 Company 13 60 5.62 Company 14 30 5.62 Company 15 30 5.55 Company 16 30 5.43 Company 17 60 5.42 Company 18 30 5.30 Company 19 60 5.31 Company 20 30 5.26 Company 21 30 5.25 Company 22 60 5.20 Company 23 30 5.22 Company 24 30 5.22 Company 25 30 5.07 Company 26 30 5.06 Company 27 60 5.10 Company 28 30 5.05 Company 29 30 4.96 Company 30 30 4.89 Company 31 30 4.86 Company 32 60 4.84 Company 33 30 4.75 Company 34 60 4.75 Company 35 30 4.70 Company 36 30 4.70 Company 37 30 4.70 Company 38 30 4.63 Company 39 30 4.61 Company 40 30 4.51 Company 41 30 4.41 Company 42 30 4.43 Company 43 30 4.36 Company 44 30 4.36 Company 45 30 4.21 Company 46 60 4.18 Company 47 30 4.17 Company 48 30 4.09 Company 49 30 4.09 Company 50 30 3.90 Company 51 30 3.82 Company 52 30 3.55 Company 53 30 3.55 Company 54 30 3.54 Company 55 60 3.46 Company 56 60 3.28 Company 57 60
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Brand Advertised
|
Time of Ad
(sec.)
|
Score
|
|
Company 1
|
60
|
6.95
|
|
Company 2
|
30
|
6.60
|
|
Company 3
|
30
|
6.56
|
|
Company 4
|
30
|
6.46
|
|
Company 5
|
30
|
6.29
|
|
Company 6
|
30
|
6.14
|
|
Company 7
|
60
|
6.12
|
|
Company 8
|
60
|
6.04
|
|
Company 9
|
60
|
6.06
|
|
Company 10
|
30
|
5.90
|
|
Company 11
|
60
|
5.73
|
|
Company 12
|
60
|
5.62
|
|
Company 13
|
60
|
5.62
|
|
Company 14
|
30
|
5.62
|
|
Company 15
|
30
|
5.55
|
|
Company 16
|
30
|
5.43
|
|
Company 17
|
60
|
5.42
|
|
Company 18
|
30
|
5.30
|
|
Company 19
|
60
|
5.31
|
|
Company 20
|
30
|
5.26
|
|
Company 21
|
30
|
5.25
|
|
Company 22
|
60
|
5.20
|
|
Company 23
|
30
|
5.22
|
|
Company 24
|
30
|
5.22
|
|
Company 25
|
30
|
5.07
|
|
Company 26
|
30
|
5.06
|
|
Company 27
|
60
|
5.10
|
|
Company 28
|
30
|
5.05
|
|
Company 29
|
30
|
4.96
|
|
Company 30
|
30
|
4.89
|
|
Company 31
|
30
|
4.86
|
|
Company 32
|
60
|
4.84
|
|
Company 33
|
30
|
4.75
|
|
Company 34
|
60
|
4.75
|
|
Company 35
|
30
|
4.70
|
|
Company 36
|
30
|
4.70
|
|
Company 37
|
30
|
4.70
|
|
Company 38
|
30
|
4.63
|
|
Company 39
|
30
|
4.61
|
|
Company 40
|
30
|
4.51
|
|
Company 41
|
30
|
4.41
|
|
Company 42
|
30
|
4.43
|
|
Company 43
|
30
|
4.36
|
|
Company 44
|
30
|
4.36
|
|
Company 45
|
30
|
4.21
|
|
Company 46
|
60
|
4.18
|
|
Company 47
|
30
|
4.17
|
|
Company 48
|
30
|
4.09
|
|
Company 49
|
30
|
4.09
|
|
Company 50
|
30
|
3.90
|
|
Company 51
|
30
|
3.82
|
|
Company 52
|
30
|
3.55
|
|
Company 53
|
30
|
3.55
|
|
Company 54
|
30
|
3.54
|
|
Company 55
|
60
|
3.46
|
|
Company 56
|
60
|
3.28
|
|
Company 57
|
60
|
|
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