the question is : give the five- number summary of each set of numbers,
7,7,5,4,1,9,8,8,8,5,2,
Are you looking for the mean, mode median, range and standard deviation?
I hope this helps. Thanks for asking.
To find the five-number summary of a set of numbers, you need to calculate the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum. The steps to find the five-number summary are as follows:
1. Arrange the set of numbers in ascending order: 1, 2, 4, 5, 5, 7, 7, 8, 8, 8, 9.
2. Minimum: The minimum is the smallest number in the set, which is 1 in this case.
3. First Quartile (Q1): The first quartile is the median of the lower half of the data set. To find Q1, you need to calculate the median of the first half. In this case, the lower half is 1, 2, 4, and 5:
- Since there is an even number of data points in the lower half, you need to find the average of the two middle terms.
- The middle terms are 2 and 4.
- The average of 2 and 4 is (2 + 4)/2 = 6/2 = 3.
So, Q1 is 3.
4. Median (Q2): The median is the middle value of the data set. In this case, the median is 5 since there are 11 data points.
5. Third Quartile (Q3): The third quartile is the median of the upper half of the data set. To find Q3, you calculate the median of the second half. In this case, the upper half is 7, 7, 8, 8, and 9:
- Again, since there is an even number of data points in the upper half, you need to find the average of the two middle terms.
- The middle terms are 7 and 8.
- The average of 7 and 8 is (7 + 8)/2 = 15/2 = 7.5.
So, Q3 is 7.5.
6. Maximum: The maximum is the largest number in the set, which is 9 in this case.
Therefore, the five-number summary for the set of numbers 7, 7, 5, 4, 1, 9, 8, 8, 8, 5, 2, is:
Minimum: 1
First Quartile (Q1): 3
Median (Q2): 5
Third Quartile (Q3): 7.5
Maximum: 9