The five number summary of a data set consists of five important descriptive statistics: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Let’s break down the calculation for the provided data set.
Given data set: 7, 11, 21, 28, 32, 33, 37, 43
- Minimum: This is the smallest number in the data set. Here, the minimum is 7.
- Maximum: This is the largest number in the data set. In this case, the maximum is 43.
- Median (Q2): The median is the middle value when the numbers are sorted. With 8 numbers (even count), the median is the average of the 4th and 5th numbers: (28 + 32) / 2 = 30.
- First Quartile (Q1): This is the median of the first half of the data (lower half). For the first half (7, 11, 21, 28), Q1 is the average of the 2nd and 3rd numbers: (11 + 21) / 2 = 16.
- Third Quartile (Q3): This is the median of the second half of the data (upper half). For the second half (32, 33, 37, 43), Q3 is the average of the 2nd and 3rd numbers: (33 + 37) / 2 = 35.
Now, we can summarize the five number summary:
- Minimum: 7
- Q1: 16
- Median (Q2): 30
- Q3: 35
- Maximum: 43
So, the five number summary for the data set is: 7, 16, 30, 35, 43.