what are the minimum, first quartile, median, third quartile, and maximum of the data set? 18 20 11 10 8 6 12 4
what are the minimum, first quartile, median, third quartile, and maximum of the data set? 18 20 11 10 8 6 12 4
a) minimum 4; first quartile 7; median 10.5; third quartile 17.5; maximum 20
b) minimum 4; first quartile 5.5; median 12.75; third quartile 15; maximum 20
c) minimum 4; first quartile 8.75; median 12.75; third quartile 17.5; maximum 20
d) minimum 4; first quartile 7; median 10.5; third quartile 15; maximum 20
a) minimum 4; first quartile 7; median 10.5; third quartile 17.5; maximum 20
To find the minimum, first quartile, median, third quartile, and maximum of a given data set, you need to follow these steps:
Step 1: Sort the data in ascending order. The data set you provided, 18, 20, 11, 10, 8, 6, 12, 4, becomes 4, 6, 8, 10, 11, 12, 18, 20.
Step 2: Calculate the minimum by selecting the smallest value in the sorted data set. In this case, the minimum is 4.
Step 3: Calculate the first quartile (Q1) by finding the median of the lower half of the data set. Since there are 8 numbers in total, the lower half is the first four numbers. The median of 4, 6, 8, and 10 is (6 + 8) / 2 = 7.
Step 4: Calculate the median by finding the middle value of the data set. Since there are 8 numbers, the median is the average of the two middle values: (10 + 11) / 2 = 10.5.
Step 5: Calculate the third quartile (Q3) by finding the median of the upper half of the data set. The upper half of the data set is 11, 12, 18, and 20. The median of these numbers is (12 + 18) / 2 = 15.
Step 6: Calculate the maximum by selecting the largest value in the sorted data set. In this case, the maximum is 20.
Therefore, for the given data set (18, 20, 11, 10, 8, 6, 12, 4), the minimum is 4, the first quartile is 7, the median is 10.5, the third quartile is 15, and the maximum is 20.
Minimum = 4
First Quartile = 7 (average of 6 and 8)
Median = 11
Third Quartile = 19 (average of 18 and 20)
Maximum = 20