The histograms show the pattern of financial aid to students at two schools.

Question

Two histograms.Short description, Two histograms.,Long description,
Histogram 1 and histogram 2 are shown. Histogram 1 starts out high, dips low and then finish high. Histogram 2 starts out low, jumps high, and then finishes low.



Histogram 1

Aid, in thousands of dollars Hundreds of students
1 8
2 2
3 1
4 2
5 3
6 2
7 3
8 2
9 2
10 4
11 4
12 7



Histogram 2
Aid, in thousands of dollars Hundreds of students
1 1
2 2
3 1
4 2
5 5
6 6
7 8
8 6
9 4
10 2
11 1
12 2



Question
Which statement about the two histograms is correct?

Answer options with 4 options
A.
Because the data sets have similar spread, means, and medians, the difference in shape is not important.

B.
Though the medians and means are similar, this similarity is misleading in that it does not reflect differences in the data sets.

C.
Because the data sets are so different in shape, there is no way to determine the relationship between the median and mean of the two data sets.

D.
Though the means of the data sets are similar, the medians are very different and this difference in medians reflects the difference in the data sets.

Answer 1

To analyze the correct statement about the two histograms, let's break down the provided information:

1. Histogram 1 shows a distribution where most financial aid amounts (in thousands of dollars) are concentrated at higher values, with higher frequencies at $10, $11, and $12 thousand, indicating more students receiving higher aid amounts.

2. Histogram 2 has a distribution that is more evenly spread across the lower to mid-range amounts, with no students receiving aid amounts greater than $12 thousand. The highest frequencies are found between $5 and $8 thousand.

Given this analysis, we should assess the provided answer options:

A. Because the data sets have similar spread, means, and medians, the difference in shape is not important.

• This statement can be dismissed because the shapes of the distributions are quite different, which means the differences in the data sets could be significant despite potential similarities in means or medians.

B. Though the medians and means are similar, this similarity is misleading in that it does not reflect differences in the data sets.

• This statement seems plausible; however, without computing the means and medians, we can't confidently affirm this without more analysis.

C. Because the data sets are so different in shape, there is no way to determine the relationship between the median and mean of the two data sets.

• This statement is incorrect. While the shapes differ, we can still explore the relationships between the median and mean.

D. Though the means of the data sets are similar, the medians are very different and this difference in medians reflects the difference in the data sets.

• This statement seems likely, especially if Histogram 1 has a higher median than Histogram 2, reflecting the greater concentration of aid at the higher end.

Based on the analysis, option D is the most accurate statement regarding the relationship between the medians and the characteristics of the two distributions.

Therefore, the answer is D.