Question

answer the questions below.

(a) on a test, each student is given a grade of a, b, c, d, or f.
which measure tells the grade given most often?
mean
median
mode

(b) greg has recorded the number of miles he has driven for each of the last 10 weeks:
381, 384, 391, 393, 396, 401, 404, 410, 411, 416.
which measure should be used to summarize the data?
mean
median
mode

(c) in the past 9 days, tammy has received the following numbers of email advertisements per day:
17, 40, 41, 43, 46, 48, 49, 51, 52.
which measure should be used to summarize the data?
mean
median
mode

Explanation:

Analyze part (a)

• Data type: Qualitative/categorical (grades \(A, B, C, D, F\)).
• Goal: Find the value occurring most frequently.
• Best measure: Mode (the only measure of center applicable to non-numerical categorical data).

Analyze part (b)

• Data set: \(381, 384, 391, 393, 396, 401, 404, 410, 411, 416\).
• Distribution: Symmetric, closely spaced, no extreme values (outliers).
• Best measure: Mean (most reliable summary for symmetric numerical data without outliers).

Analyze part (c)

• Data set: \(17, 40, 41, 43, 46, 48, 49, 51, 52\).
• Distribution: Contains a significant outlier on the lower end (\(17\)), while other values are clustered between \(40\) and \(52\).
• Best measure: Median (not affected by extreme outliers, unlike the mean).

Answer:

Question a

• Mean
• Median
• Mode (Correct answer)

Question b

• Mean (Correct answer)
• Median
• Mode

Question c

• Mean
• Median (Correct answer)
• Mode