Question

1. make a histogram from this data, which lists all the scores a basketball team had in the games in one season. make six bins.

60 62 68 71 72 72 73 74 74 74 75 75 76 77 77 77
78 78 78 79 79 81 81 82 83 83 85 86 88 90 92 95

score frequency
60 - 65 11
60 - 71 11
71 - 77 11 11
78 - 83 11 11
84 - 89 111
90 - 95 111

1. a. as this distribution in problem 2 has its peak near the center, you could use either mean or median as a measure of center. this time, find the median and the interquartile range.

median ________ interquartile range ________
b. describe the variation in the data. is it very scattered (varied), somewhat so, or not very much so?

Explanation:

Step1: Organize data

First, we have a total of \(n = 30\) data - points: \(60,62,68,71,72,72,73,74,74,74,75,75,76,77,77,77,78,78,78,79,79,81,81,82,83,83,85,86,88,90,92,95\).

Step2: Find the median

Since \(n = 30\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}=15\)th and \((\frac{n}{2}+1) = 16\)th ordered data values. The 15th value is \(77\) and the 16th value is \(77\), so the median \(M=\frac{77 + 77}{2}=77\).

Step3: Find the first and third quartiles

The lower half of the data (the first 15 values) is: \(60,62,68,71,72,72,73,74,74,74,75,75,76,77,77\). The median of the lower half (\(Q_1\)) is the 8th value, so \(Q_1 = 74\). The upper half of the data (the last 15 values) is: \(77,78,78,78,79,79,81,81,82,83,83,85,86,88,90,92,95\). The median of the upper half (\(Q_3\)) is the 8th value of the upper - half, so \(Q_3 = 83\).

Step4: Calculate the inter - quartile range

The inter - quartile range \(IQR=Q_3 - Q_1\). Substituting \(Q_1 = 74\) and \(Q_3 = 83\), we get \(IQR=83 - 74 = 9\).

Step5: Describe the variation

The data has a relatively small variation. The scores are mostly clustered around the median. The range of the data is \(95−60 = 35\), but the inter - quartile range is only 9, indicating that the middle 50% of the data is not very spread out. So, the data is not very scattered.

Answer:

Median: \(77\)
Inter - quartile range: \(9\)
The data is not very scattered.