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What is the interquartile range of the following data set?

45, 12, 48, 96, 61, 84, 29, 1,72,5,14
a.45
b.33
c.27
d.60
(apex)

User Ajay Takur
by
4.1k points

1 Answer

4 votes

Answer:

The interquartile range is 60 ⇒ D

Explanation:

The interquartile range is the difference between the upper quartile and the lower quartile

Let us explain how to find the interquartile range

  1. Arrange the number from smallest to greatest
  2. Find its median Q1 (the middle number in the set of numbers)
  3. Find the lower quartile Q1 which is the median of the set of the numbers before the median
  4. Find the upper quartile Q3 which is the median of the set of the numbers after the median
  5. Subtract Q1 from Q3 the answer is the interquartile range

Let us do these steps to find it

∵ The data set is {45, 12, 48, 96, 61, 84, 29, 1, 72, 5, 14}

→ Arrange them

∴ The data set is {1, 5, 12, 14, 29, 45, 48, 61, 72, 84, 96}

∵ They are 11 numbers

∴ The middle number is the 6th number (5 before it and 5 after it)

∵ The 6th number is 45

The median is 45

→ Find the lower set (before the median)

∴ The lower set is {1, 5, 12, 14, 29}

→ Find the lower quartile Q1

∵ The lower quartile is the middle number in this set

∵ There are 5 numbers

∴ The middle one is the 3rd

∵ The 3rd is 12

Q1 = 12

→ Find the upper set (after the median)

∴ The upper set is {48, 61, 72, 84, 96}

→ Find the upper quartile Q3

∵ The upper quartile is the middle number in this set

∵ There are 5 numbers

∴ The middle one is the 3rd

∵ The 3rd is 72

Q3 = 72

→ Subtract them to find the interquartile range

∵ The interquartile range = Q3 - Q1

∴ The interquartile range = 72 - 12

The interquartile range = 60

User Chakrapani
by
4.6k points