Question

the stemplot displays 26 students scores on a 90 - point statistics test. which of the following best describes the center and variability of the distribution? test scores 4 3 4 5 6 5 1 2 3 5 5 7 6 0 3 3 6 5 6 7 7 9 9 7 1 1 2 4 7 6 7 9 8 4 8 5 key: 6|8 = 68 points the scores on the test are centered around 63 and vary from 45 to 85. the scores on the test are centered around 66 and vary from 43 to 85. the scores on the test are centered around 66 and vary from 40 to 80. the scores on the test are centered around 69 and vary from 45 to 85.

Explanation:

Step1: Find the minimum and maximum values

In a stemplot, the minimum value is the first leaf on the first stem. Here, the minimum value is \(43\). The maximum value is the last leaf on the last stem, which is \(85\).

Step2: Find the median (center)

Since there are \(n = 26\) data points, the median is the average of the \(13^{th}\) and \(14^{th}\) ordered values.
Counting the leaves:

• Stem \(4\): \(2\) leaves (\(43,45,46\))
• Stem \(5\): \(5\) leaves (\(51,52,53,55,57\))
• Stem \(6\): \(6\) leaves (\(60,63,63,65,66,67,67,69,69\))
• Stem \(7\): \(7\) leaves (\(71,71,72,74,76,77,79\))
• Stem \(8\): \(2\) leaves (\(84,85\))

The \(13^{th}\) value is \(66\) and the \(14^{th}\) value is \(66\). The median \(\frac{66 + 66}{2}=66\)

Answer:

The scores on the test are centered around \(66\) and vary from \(43\) to \(85\) (the second option).