Question

question 5
0/1 pt 2 details
find the 5 number summary for the data shown
12 29
34 47
55 59
61 63
90 93
97 98
5 number summary:
boxes, boxes, boxes, boxes, boxes
use the locator/percentile method described in your book, not your calculator.
check answer

Explanation:

Step1: List and sort the data

First, we list all the data points: 12, 29, 34, 47, 55, 59, 61, 63, 90, 93, 97, 98. Then we sort them (they are already in order here). The number of data points \( n = 12 \).

Step2: Find the minimum

The minimum value is the smallest number in the dataset. So, minimum \( = 12 \).

Step3: Find the first quartile (Q1)

The locator for Q1 is \( L_{25}=\frac{25}{100}\times n=\frac{25}{100}\times12 = 3 \). Since \( L_{25} \) is an integer, Q1 is the average of the \( 3^{\text{rd}} \) and \( 4^{\text{th}} \) values. The \( 3^{\text{rd}} \) value is 34 and the \( 4^{\text{th}} \) value is 47. So, \( Q1=\frac{34 + 47}{2}=\frac{81}{2}=40.5 \).

Step4: Find the median (Q2)

The locator for the median (Q2, 50th percentile) is \( L_{50}=\frac{50}{100}\times n=\frac{50}{100}\times12 = 6 \). Since \( L_{50} \) is an integer, the median is the average of the \( 6^{\text{th}} \) and \( 7^{\text{th}} \) values. The \( 6^{\text{th}} \) value is 59 and the \( 7^{\text{th}} \) value is 61. So, \( \text{Median}=\frac{59+61}{2}=\frac{120}{2} = 60 \).

Step5: Find the third quartile (Q3)

The locator for Q3 is \( L_{75}=\frac{75}{100}\times n=\frac{75}{100}\times12=9 \). Since \( L_{75} \) is an integer, Q3 is the average of the \( 9^{\text{th}} \) and \( 10^{\text{th}} \) values. The \( 9^{\text{th}} \) value is 90 and the \( 10^{\text{th}} \) value is 93. So, \( Q3=\frac{90 + 93}{2}=\frac{183}{2}=91.5 \).

Step6: Find the maximum

The maximum value is the largest number in the dataset. So, maximum \( = 98 \).

Answer:

\( 12 \), \( 40.5 \), \( 60 \), \( 91.5 \), \( 98 \)