Problem

Given the set of data: \(14, 16, 16, 18, 19, 20, 21, 21, 22, 24, 25, 27\). Find the average, the descriptive statistics, and the interquartile range (H-Spread).

Answer

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Answer

Step 4: The interquartile range (H-Spread) is the difference between Q3 and Q1. \[23 - 17 = 6\]

Steps

Step 1 :Step 1: Find the average (mean) by adding all the numbers together and then dividing by the count of the numbers. \[\frac{14 + 16 + 16 + 18 + 19 + 20 + 21 + 21 + 22 + 24 + 25 + 27}{12} = 20.33\]

Step 2 :Step 2: Organize the data in ascending order to find the median (the middle number). Since there are 12 numbers, the median is the average of the 6th and 7th numbers. \[\frac{20 + 21}{2} = 20.5\]

Step 3 :Step 3: To find the quartiles, divide the data set into two halves. The first quartile (Q1) is the median of the first half and the third quartile (Q3) is the median of the second half. \[Q1 = \frac{16 + 18}{2} = 17,\ Q3 = \frac{22 + 24}{2} = 23\]

Step 4 :Step 4: The interquartile range (H-Spread) is the difference between Q3 and Q1. \[23 - 17 = 6\]

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