Question

Which is different? Find "both" answers. 53, 47, 60, 45, 62, 59, 65, 50, 56, 48 What is the interquartile range of the data? What is the range of the middle half of the data? What is the range of the data? What is the difference between the third quartile and the first quartile? Question 2 Answer of the "different" question: Answer of the "same" three questions:

Answer 1

The range of the middle half of the data is 12

The difference between the third quartile and the first quartile is 12.75

Explanation:

Here, we sort the data as follows;

45

47

48

50

53

56

59

60

62

65

The five numbers are;

Minimum = 45

Maximum = 65

1st quartile, Q₁ = (n + 1)/4th term = 47.75

2nd quartile, Q₂ = Median = (n + 1)/2 th term = 54.5

3rd quartile, Q₃ = Median = 3(n + 1)/4th term = 60.5

The Interquartile range = Q₃ - Q₃ = 60.5 - 47.75 = 12.75

The middle half is from the 2.5th term to the 7.5th given as follows;

2.5th term = 47.5

7.5th term = 59.5

The range of the middle half of the data = 59.5 to 47.5 which is 59.5 - 47.5 = 12

The range of the middle half of the data = 12

The difference between the third quartile and the first quartile is equal to Q₃ - Q₁ = 12.75.

Answer 2

Answer of the "different" question is 20

Answer of the "same" three questions: 12.

Explanation:

The interquartile range is found by

Order the data from least to greatest: 45, 47, 48, 50, 53, 56, 59, 60, 62, 65

Find the median the median in this case is 53+56 / 2 = 54.5

Calculate the median of both the lower and upper half of the data: the median of the lower half 45, 47, 48, 50, 53 is 48 (first quartile) while the median of the upper half 56, 59, 60, 62, 65 (third quartile) is 60.

Thus, the interquartile range is the difference between the upper and lower medians: 60 - 48 = 12.

The range of the middle half of the data is also the interquartile range which is 12.

The range of the data set is the largest data minus the least: 65 - 45 = 20.

The different question among all these is the range of the data set which is 20.

Answer of the same three: What is the interquartile range of the data?

What is the range of the middle half of the data?

What is the difference between the range of the third quartile and the range of the first quartile?

Answer is 12