Question

for all of the colleges in this data set there is variability in on-time graduation rates from year to year. when we compare the colleges, there is also a lot of overlap in the distributions. yet we can still distinguish substantial differences among some of them.
e) pick two colleges that you think differ substantially in on-time graduation rates. use the boxplots (and 5-number summaries) to provide at least 3 observations to support your choice.
f) pick two colleges that you think have a similar distribution of on-time graduation rates. use the boxplots (and 5-number summaries) to provide at least 3 observations to support your choice.
(table: college | n | min | q1 | q2 | q3 | max; a | 8 | 43.2 | 50.5 | 63.75 | 71.1 | 73.8; b | 8 | 67.3 | 69.5 | 70.15 | 73.5 | 76.7; c | 8 | 54.5 | 56.25 | 67.65 | 72.15 | 74.8; d | 8 | 74.1 | 76 | 79 | 82.1 | 84.6; e | 8 | 54.5 | 56.25 | 59.15 | 64.8 | 71.3; f | 8 | 57.7 | 63.7 | 72 | 82.85 | 87.4; boxplot with colleges a-f, x-axis percent that graduate ontime 40–90)

Explanation:

Part (e)

Let's choose College A and College D.

1. Minimum Value: College A has a minimum of 43.2, while College D has a minimum of 74.1. This shows a large gap in the lowest on - time graduation rates between the two.
2. Median (Q2): The median for College A is 63.75, and for College D it is 79. The median of D is much higher than that of A, indicating that the middle - value graduation rate of D is significantly higher.
3. Maximum Value: College A's maximum is 73.8, and College D's maximum is 84.6. The highest graduation rate of D is also much higher than that of A.

Let's choose College C and College E.

1. Minimum Value: Both College C and College E have a minimum value of 54.5.
2. Q1 (First Quartile): The first quartile for College C is 56.25, and for College E it is also 56.25.
3. Shape of Boxplots: From the boxplots, the position and spread of the boxes (representing the inter - quartile range) for College C and College E appear to be similar, which is consistent with their 5 - number summaries.

Answer:

Two colleges with substantial differences in on - time graduation rates are College A and College D.

• Observation 1: Min of A is 43.2, Min of D is 74.1 (large difference in lowest rates).
• Observation 2: Q2 (median) of A is 63.75, Q2 of D is 79 (D has a much higher middle - value rate).
• Observation 3: Max of A is 73.8, Max of D is 84.6 (D has a much higher highest rate).

Part (f)