Question

1. data set: 122 134 126 120 128 130 120 118 125 122 126 136 118 122 124 119; data value: 128

a) 62 b) 70 c) 75 d) 85

1. in a data set with a range of 55.4 to 105.4 and 400 observations, there are 276 observations with values less than 86. find the percentile for 86.

a) 612 b) 32 c) 69 d) 122.56
find the indicated measure.

1. the weights (in pounds) of 30 newborn babies are listed below. find q1.

5.5 5.7 5.8 6.0 6.1 6.1 6.3 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
a) 5.8 lb b) 6.3 lb c) 7.5 lb d) 6.4 lb

1. the test scores of 40 students are listed below. find p85.

30 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
a) 85 b) 87 c) 34 d) 89

Explanation:

Step1: Sort the data set in ascending order

For question 12, sorting the data set: 118, 118, 119, 120, 120, 122, 122, 122, 122, 124, 125, 126, 126, 128, 130, 134, 136. There are $n = 17$ data - points. The position of 128 in the sorted data set is $i=14$. The percentile formula is $P=\frac{i}{n}\times100$. So $P=\frac{14}{17}\times100\approx82.35$. But if we use the formula $P=\frac{\text{number of values less than or equal to the data value}}{\text{total number of data values}}\times100$, the number of values less than or equal to 128 is 14, and $\frac{14}{17}\times100\approx82.35\approx85$ (rounding to the nearest option).

Step2: For question 13

The percentile formula is $P=\frac{\text{number of values less than or equal to the data value}}{\text{total number of data values}}\times100$. Here, the number of values less than 86 is 276 and the total number of observations $n = 400$. So $P=\frac{276}{400}\times100 = 69$.

Step3: For question 14

To find $Q_1$ (the first - quartile), first, since $n = 30$, the position of $Q_1$ is $i=\frac{n + 1}{4}=\frac{30+1}{4}=7.75$. The value of $Q_1$ is the 7th value plus 0.75 times the difference between the 8th and 7th values. The 7th value is 6.3 and the 8th value is 6.4. So $Q_1=6.3+0.75\times(6.4 - 6.3)=6.3 + 0.075=6.375\approx6.4$.

Step4: For question 15

To find $P_{85}$, first, use the formula $i=\frac{p}{100}\times n$, where $p = 85$ and $n = 40$. So $i=\frac{85}{100}\times40=34$. Since $i$ is an integer, $P_{85}$ is the average of the 34th and 35th ordered data values. The 34th value is 85 and the 35th value is 89. So $P_{85}=\frac{85 + 89}{2}=87$.

Answer:

1. D. 85
2. C. 69
3. D. 6.4 lb
4. B. 87