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What is the five-number summary for the data set?

Data set: 1, 3, 4, 4, 5, 10, 12, 13, 14, 16, 19, 21, 23, 27, 30, 31, 31, 33, 44, 46, 51, 55, 58

Options:
A. 1, 10, 23, 33, 58
B. 1, 10, 21, 33, 58
C. 1, 11, 23, 38.5, 58
D. 1, 11, 21, 33, 38.5, 58

Answer :

The five number summary for the data set is:

Minimum =1

Q1=10

Median =22

Q3=35.75

Maximum =58

Given data:

Five number summary from the following data

1,3,4,4,5,10,12,13,14,16,19,21,23,27,30,31,31,33,44,46,51,55,58,1,10,23,33,58,1,10,21,33,58,1,11,23,38.5,58,1,11,21,33,38.5,58

Arrange the numbers in ascending order

1,1,1,1,1,3,4,4,5,10,10,10,11,11,12,13,14,16,19,21,21,21,23,23,23,27,30,31,31,33,33,33,33,38.5,38.5,44,46,51,55,58,58,58,58,58

Step-2: Find the minimum value

Minimum =1 (the smallest number)

Step-3: Find the maximum value

Maximum =58 (the largest number)

Step-4: Find the median

The median is the middle number in a sorted data set and N is the total number of elements

If N is odd then the median is a single middle number, and if N is even then the median is the average of the two middle numbers.

1,1,1,1,1,3,4,4,5,10,10,10,11,11,12,13,14,16,19,21,21,21,23,23,23,27,30,31,31,33,33,33,33,38.5,38.5,44,46,51,55,58,58,58,58,58

N=44 is even, so median is the average of the two middle numbers at position 22 and 23

We have 21+232=22

Median =22

Step-5: Place parentheses around the numbers above and below the median.

{1,1,1,1,1,3,4,4,5,10,10,10,11,11,12,13,14,16,19,21,21,21},{23,23,23,27,30,31,31,33,33,33,33,38.5,38.5,44,46,51,55,58,58,58,58,58}

Step-6: Find Q1 by finding the median for lower half of data(left of the median)

1,1,1,1,1,3,4,4,5,10,10,10,11,11,12,13,14,16,19,21,21,21

N=22 is even, so median is the average of the two middle numbers at position 11 and 12

We have 10+102=10

∴Q1=10

Step-7: Find Q3 by finding the median for upper half of data(right of the median)

23,23,23,27,30,31,31,33,33,33,33,38.5,38.5,44,46,51,55,58,58,58,58,58

N=22 is even, so median is the average of the two middle numbers at position 11 and 12

We have 33+38.52=35.75

∴Q3=35.75

Step-8: Summary found in the above steps.

Minimum =1

Q1=10

Median =22

Q3=35.75

Maximum =58

Hence, the five number summary is solved.

To learn more about five number summary, refer:

https://brainly.com/question/37558753

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