The Five number summary for the given data:
Minimum: 24
Lower quartile: Q1 = 29
Median: 43
Upper quartile: Q3 = 50
Maximum: 56
Interquartile range: IQR = 21
What is the interquartile range?
The interquartile range is calculated by
IQR = Q3 - Q1
Where Q3 - upper quartile and Q1 - lower quartile
Q3 = 3/4(n + 1) th term
Q1 = 1/4(n + 1) th term
Calculation:
The given data points are
24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56
where n = 13
Maximum data value = 56
Minimum data value = 24
Calculating Median:
Median = (n+1)/2 th term
⇒ Median = (13 + 1)/2 = 7th term
∴ Median = 43
Calculating the quartiles:
Upper quartile Q3 = 3/4(n + 1)th term
⇒ Q3 = 3/4(13 + 1) = 10.5
⇒ Q3 = 10th term + 1/2(11th term - 10th term)
⇒ Q3 = 49 + 1/2(51 - 49)
⇒ Q3 = 49 + 1
∴ Q = 50
Lower quartile Q1 = 1/4(n + 1)th term
⇒ Q1 = 1/4(13 + 1) = 3.5
⇒ Q1 = 3rd term + 1/2(4th term - 3rd term)
⇒ Q1 = 29 + 1/2(29 - 29)
∴ Q1 = 29
Calculating the IQR:
IQR = Q3 - Q1
= 50 - 29
= 21
Thus, the interquartile range is 21.
Therefore, the five-number summary for the given data:
Minimum: 24
Lower quartile: Q1 = 29
Median: 43
Upper quartile: Q3 = 50
Maximum: 56
Interquartile range: IQR = 21
Learn more about the five-number summary here:
https://brainly.com/question/17110151
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