Question

Compare the two distributions given by the 5 -number summaries below. Based on these 5 - numbers summaries, select the best choice from those given. HINT: Draw the two boxplots using the 5-number summaries. Compare the shapes. Compare the ranges. Compare the Medians. These comparisons will help greatly in answering this question.

Distribution A : Min. =3,Q1=15, Med. =17,Q3=19, Max. =30
Distribution B: Min. =13,Q1=15, Med. =17,Q3=19, Max. =21
1.. The mean of Distribution A= the mean of Distribution B.
2. The relationship between the means cannot be determined.
3. The mean of Distribution A< the mean of Distribution B.
4. The mean of Distribution A> the mean of Distribution

Answer 1

The range of Distribution A is greater than the range of Distribution B.

Both distributions have the same median

2. The relationship between the means cannot be determined.

Comparing the boxplots

Both distributions have the same minimum, first quartile (Q1), median, third quartile (Q3). But different maixmum

The range of distribution A is 30 - 3 = 27

The range of distribution B is 21 - 13 = 8

The range of distribution A is greater than the range of distribution B

Both distributions have the same median = 17

The relationship between the means cannot be determined. We cannot definitively determine the relationship between the means based solely on the summaries.