Question

1. thirteen golfers were asked what their score was on their last game. the scores are shown below. 86, 75, 72, 85, 78, 88, 74, 74, 83, 85, 77, 57, 77

find the range and the outlier(s), if any, of the golfers scores.
a. range 32; no outliers
b. range 31; outlier 57
c. range 32; outlier 57
d. range 31; no outliers

1. using the data set 17, 25, 30, 27, 16, 19, 35, 42, 18, 20, 19, and 13, what value corresponds to the 31st percentile?

a. 18 b. 27 c. 17 d. 30

1. the following distribution lists ages of students in a college business class. class limits frequency

20 - 26 7
27 - 33 12
34 - 40 9

Explanation:

Step1: Find the range for golfers' scores

First, order the scores: 57, 72, 74, 74, 75, 77, 77, 77, 78, 83, 85, 85, 88. The range is calculated as the maximum - minimum value. So, range = 88 - 57 = 31.

Step2: Check for outliers

To check for outliers, we first find the first quartile ($Q_1$) and the third quartile ($Q_3$). The median of the lower half of the data (57, 72, 74, 74, 75, 77) is $Q_1 = 74$. The median of the upper half of the data (77, 78, 83, 85, 85, 88) is $Q_3 = 83$. The inter - quartile range (IQR) = $Q_3 - Q_1=83 - 74 = 9$. The lower fence for outliers is $Q_1-1.5\times IQR=74 - 1.5\times9=74 - 13.5 = 60.5$. The upper fence for outliers is $Q_3 + 1.5\times IQR=83+1.5\times9=83 + 13.5 = 96.5$. Since 57 < 60.5, 57 is an outlier.

Step3: Find the 31st percentile for the second data set

First, order the data set: 13, 16, 17, 18, 19, 19, 20, 25, 27, 30, 35, 42. There are $n = 12$ data points. The index $i$ for the $p$th percentile is calculated as $i=\frac{p}{100}\times n$. For $p = 31$ and $n = 12$, $i=\frac{31}{100}\times12=3.72$. Rounding up, we look at the 4th value in the ordered data set, which is 18.

Answer:

1. b. range 31; outlier 57
2. a. 18