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Information
This data represents the number of hamburgers sold over the last 10 days at a restaurant.



34, 37, 41, 51, 56, 58, 70, 75, 77, 77

Question
What is the interquartile range? Enter the answer in the box.

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hamburgers sold

1 answer

To find the interquartile range (IQR), we need to first find the first quartile (Q1) and the third quartile (Q3) from the given data set.

The given data is: 34, 37, 41, 51, 56, 58, 70, 75, 77, 77

  1. Order the data (which is already ordered): 34, 37, 41, 51, 56, 58, 70, 75, 77, 77

  2. Find the median (Q2):

    • The median (Q2) falls between the 5th and 6th values in this ordered list since there are 10 data points.
    • Q2 = (56 + 58) / 2 = 57

  3. Find Q1:

    • Q1 is the median of the lower half (first 5 values): 34, 37, 41, 51, 56.
    • The median of this set is the 3rd value: Q1 = 41.

  4. Find Q3:

    • Q3 is the median of the upper half (last 5 values): 58, 70, 75, 77, 77.
    • The median of this set is the 3rd value: Q3 = 75.

  5. Calculate the interquartile range (IQR):

    • IQR = Q3 - Q1 = 75 - 41 = 34.

So, the interquartile range is 34.