Answer:
4
Step-by-step explanation:
20 is the median
so before and after 20 is the Q3 and Q1
Q1 is 18
Q3 is 22
22 minus 18
The Interquartile range, IQR of the numbers is 4
The process of calculating the above Interquartile Range, IQR is as follows;
The given numbers in the data set are;
17, 18, 18, 19, 20, 21, 21, 23, 25
The required information;
Calculate the inter quartile range IQR = Q₃ - Q₁
The method;
The numbers in the data set are to be arranged in increasing order from smallest to largest number to give;
17, 18, 18, 19, 20, 21, 21, 23, 25 (The numbers were already arranged)
The values of first quartile, Q₁, and the third quartile, Q₃ are then found as follows;
The first quartile, Q₁ = The (n + 1)/4 th term
The third quartile, Q₃ = The 3·(n + 1)/4 th term
Where;
n = The number count in the data set = 9
Therefore:
Q₁ = The (9 + 1)/4 = The 2.5 th term = 18 + (18 - 18) × 0.5 = 18
Q₃ = The 3 × (9 + 1)/4 th term = 7.5 th term = 21 + (23 - 21) × 0.5 = 22
IQR = Q₃ - Q₁
Therefore;
IQR = 22 - 18 = 4
The Interquartile Range, IQR = 4
The Box and Whiskers plot of the above data created with MS Excel is
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