Problem

Given the following set of data {7, 9, 13, 15, 16, 20, 21, 23, 24, 25, 29, 30, 31, 32, 33, 34, 36, 38, 43, 50}, find the five number summary (minimum, first quartile, median, third quartile, maximum).

Solution

Step 1 :First, we arrange the data in increasing order, which has already been done for us.

Step 2 :The minimum value is the first number in the data set: \( 7 \)

Step 3 :The maximum value is the last number in the data set: \( 50 \)

Step 4 :The median (second quartile, Q2) is the middle value. Since we have 20 numbers, the median is the average of the 10th and 11th numbers: \( \frac{25 + 29}{2} = 27 \)

Step 5 :The first quartile (Q1) is the median of the first half of the data. Since we have 10 numbers in the first half, we take the average of the 5th and 6th numbers: \( \frac{16 + 20}{2} = 18 \)

Step 6 :The third quartile (Q3) is the median of the second half of the data. We take the average of the 15th and 16th numbers: \( \frac{33 + 34}{2} = 33.5 \)

From Solvely APP
Source: https://solvelyapp.com/problems/jum655rEB3/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download