Answer:
The interquartile range is 60 ⇒ D
Step-by-step explanation:
The interquartile range is the difference between the upper quartile and the lower quartile
Let us explain how to find the interquartile range
- Arrange the number from smallest to greatest
- Find its median Q1 (the middle number in the set of numbers)
- Find the lower quartile Q1 which is the median of the set of the numbers before the median
- Find the upper quartile Q3 which is the median of the set of the numbers after the median
- 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
