Business Studies
The most frequently used measures of central tendency for quantitative data are the mean and the median. The following table shows civil service examination scores from 24 applicants to law enforcement jobs:
83 74 85 79
82 67 78 70
18 93 64 27
93 98 82 78
68 82 83 99
96 62 93 58
Using Excel, find the mean, standard deviation, and 5-number summary of this sample.
• Construct and paste a box plot depicting the 5-number summary.
• Does the dataset have outliers? If so, which one(s)?
• Would you prefer to use the mean or the medians this dataset’s measure of central tendency? Why?
ANSWER
The most frequently used measures of central tendency for quantitative data are the mean and the median. The following table shows civil service examination scores from 24 applicants to law enforcement jobs:
83 74 85 79
82 67 78 70
18 93 64 27
93 98 82 78
68 82 83 99
96 62 93 58
Using Excel, find the mean, standard deviation, and 5-number summary of this sample.
Answer
Mean = 75.5
Standard deviation = 19.9913
The 5-number summary comprises of the minimum, first quartile, median, third quartile, and maximum. These are as shown below:
Minimum = 18
First quartile = 67.75
Median = 80.5
Third quartile = 87
Maximum = 99
- Construct and paste a box plot depicting the 5-number summary.
The box plot is as shown below
- Does the dataset have outliers? If so, which one(s)
Outliers are located outside the whiskers. Therefore, the boxplot does not show the presence of outliers.
- Would you prefer to use the mean or the medians this dataset’s measure of central tendency? Why?
Median.
This is because the boxplot shows that the dataset is skewed. Median is the appropriate measure of central tendency that will accurately describe the data. Mean inaccurately describes skewed data.
