Which set of temperature data has the largest dispersion as measured by its interquartile range?

1) 15, 17, 19, 21, 21, 22, 28
2) 21, 23, 36, 37, 44, 48, 50
3) 10, 19, 22, 23, 23, 29, 44
4) 42, 47, 49, 50, 52, 59, 60

22-17= 5
48-23= 25
29-19= 10
59-47= 12

Answered by yucolee | 2024-06-24

The correct option is 2. 21,23,36,37,44,48,50 set of data of temperatures has the largest dispersion as measured by its interquartile range.
Set 1: 15, 17, 19, 21, 21, 22, 28

Ordered: 15, 17, 19, 21, 21, 22, 28

Median: 21 (middle value)

( Q1 ): Median of the first half (15, 17, 19), which is 17

( Q3 ): Median of the second half (21, 22, 28), which is 22

IQR: ( Q3 - Q1 = 22 - 17 = 5 )


Set 2: 21, 23, 36, 37, 44, 48, 50

Ordered: 21, 23, 36, 37, 44, 48, 50

Median: 37 (middle value)

( Q1 ): Median of the first half (21, 23, 36), which is 23

( Q3 ): Median of the second half (44, 48, 50), which is 48

IQR: ( Q3 - Q1 = 48 - 23 = 25 )


Set 3: 10, 19, 22, 23, 23, 29, 44

Ordered: 10, 19, 22, 23, 23, 29, 44

Median: 23 (middle value)

( Q1 ): Median of the first half (10, 19, 22), which is 19

( Q3 ): Median of the second half (23, 29, 44), which is 29

IQR: ( Q3 - Q1 = 29 - 19 = 10 )


Set 4: 42, 47, 49, 50, 52, 59, 60

Ordered: 42, 47, 49, 50, 52, 59, 60

Median: 50 (middle value)

( Q1 ): Median of the first half (42, 47, 49), which is 47

( Q3 ): Median of the second half (52, 59, 60), which is 59

IQR: ( Q3 - Q1 = 59 - 47 = 12 )


Summary of IQR calculations:

Set 1 IQR: 5

Set 2 IQR: 25

Set 3 IQR: 10

Set 4 IQR: 12


The set of data with the largest dispersion as measured by its interquartile range is Set 2, with an IQR of 25.

Answered by Yakavi | 2024-07-02

The set of temperature data with the largest dispersion, as measured by its interquartile range, is Set 2 with an IQR of 25. The calculations for each set revealed that the IQR for each varied, confirming Set 2's wider spread. Understanding the IQR helps in analyzing how data is distributed around the median.
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Answered by Yakavi | 2024-12-24