Answer:
Part A:
The interquartile range is approximately 10
Part B:
The difference between the median values for each data set is approximately 6
Part C:
i) More widely distributed and concentrated to the beginning of the month
The better measure of the center for the male dataset is the median
ii) The skewed distribution
The mean is the better measure of center for the dataset
Part D;
A possible reason for the outlier is by chance
Step-by-step explanation:
Part A:
The interquartile range, IQR, is the width of the box in the box plot = The difference between the third quartile, Q₃ and the first quartile, Q₁ = Q₃ - Q₁
From the diagram, Q₃ ≈ 13, Q₁ ≈ 3
∴ The interquartile range, IQR = 13 - 3 = 10
Part B:
From the diagram of the box plot, the median value, of the males, M-Q₂ ≈ 12
The median value for the females, F-Q₂ ≈ 18
The difference, M-Q₂ - F-Q₂ = 18 - 12 ≈ 6
The difference between the median values for each data set, d = M-Q₂ - F-Q₂ ≈ 6
Part C:
i) The distribution of the of the male dataset for the male has more data on the left of the box plot, with the median located approximately at the center and an outlier at end of the month
The better measure of the center for the male dataset is the median
ii) The distribution of the dataset for the females is skewed (concentrated on the right of the plot). The data set has no outlier and the first quartile is 0, while the third quartile corresponds with the maximum value at 21, the first quartile is 15 and the IQR is approximately 6
The better measure of center for the dataset is the mean, as the difference between the value of the first quartile, 0, and the other data points is more accounted for by the mean
Part D;
The possible reason for the outlier in the male dataset can be attributed to chance
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