Answer:
The correct option is;
Both spreads are best described by the standard deviation
Step-by-step explanation:
The given information are;
, College High School
High, 20 20
Low, 6 3
Q₁, 8 5.5
Q₃, 18 16
IQR, 10 10.5
Median, 14 11
Mean, 13.3 11
σ, 5.2 5.4
Checking for outliers, we have
College
Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7
Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33
For high school
Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25
Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75
Therefore, there are no outliers and the data is representative of the population
From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2
The difference between the low and the high is also approximately 3 standard deviations
Therefore the college spread is best described by the standard deviation
Similarly for the high school students, the IQR is approximately two standard deviations, the difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4
Therefore the high school spread is also best described by the standard deviation.
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