Question

Calculate the five-number summary of the given data. use the approximation method. 7,9,21,1,12,18,21,23,12,17,9,11,6,3

Answer 1

To calculate the five-number summary of the data, arrange the numbers in ascending order, find the minimum and maximum, and then calculate the median (Q2), first (Q1), and third (Q3) quartiles. The summary consists of Min, Q1, Q2, Q3, and Max.

Step-by-step explanation:

Five-Number Summary Calculation

To calculate the five-number summary of the given data set (7, 9, 21, 1, 12, 18, 21, 23, 12, 17, 9, 11, 6, 3), you will need to follow these steps:

1. Arrange the data in ascending order: 1, 3, 6, 7, 9, 9, 11, 12, 12, 17, 18, 21, 21, 23.
2. Identify the minimum (Min) which is the smallest number: Min = 1.
3. Identify the maximum (Max) which is the largest number: Max = 23.
4. Find the median (Q2) which is the middle value of the data set: Q2 = (11 + 12) / 2 = 11.5.
5. Find the first quartile (Q1) which is the median of the first half of the data: Q1 = (6 + 7) / 2 = 6.5.
6. Find the third quartile (Q3) which is the median of the second half of the data: Q3 = (18 + 21) / 2 = 19.5.

The five-number summary is: Min = 1, Q1 = 6.5, Q2 = 11.5, Q3 = 19.5, Max = 23.