Question

Following are the number of grams of carbohydrates in a sample of 12-ounce espresso beverages offered at Starbucks.

6, 7, 19 , 20, 22, 25, 27, 38 , 48, 59

Compute the IQR. Write only a number as your answer.

Answer 1

Solution: Given that 6, 7, 19 , 20, 22, 25, 27, 38 , 48, 59

Explanation :

The interquartile range is the difference between the third and first quartiles.

The third quartile is 38.

The first quartile is 19.

The interquartile range = 38 - 19 = 19.

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The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

6 7 19 20 22 25 27 38 48 59   

So, the bottom half is

6 7 19 20 22   

The median of these numbers is 19.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

6 7 19 20 22 25 27 38 48 59   

So, the upper half is

25 27 38 48 59   

The median of these numbers is 38.