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The data below represents the number of customers at each Spaghetti Shop.

24,25,29,30,31,31,32,34,34
Which box plot correctly summarizes the data?

The data below represents the number of customers at each Spaghetti Shop.\newline24,25,29,30,31,31,32,34,34 24,25,29,30,31,31,32,34,34 \newlineWhich box plot correctly summarizes the data?

Full solution

Q. The data below represents the number of customers at each Spaghetti Shop.\newline24,25,29,30,31,31,32,34,34 24,25,29,30,31,31,32,34,34 \newlineWhich box plot correctly summarizes the data?
  1. Calculate the Median: Calculate the median of the data set.\newlineThe median is the middle number when the numbers are listed in order.\newlineSince there are 99 numbers, the median is the 55th number.\newlineThe 55th number in the ordered list is 3131.
  2. Find First Quartile: Find the first quartile (Q1Q_1).\newlineThe first quartile is the median of the first half of the data.\newlineThe first half of the data is 2424, 2525, 2929, 3030.\newlineThe median of this half is the average of 2525 and 2929.\newlineQ1=(25+29)/2=27Q_1 = (25 + 29) / 2 = 27.
  3. Determine Third Quartile: Determine the third quartile (Q3Q_3).\newlineThe third quartile is the median of the second half of the data.\newlineThe second half of the data is 3131, 3232, 3434, 3434.\newlineThe median of this half is the average of 3232 and 3434.\newlineQ3=(32+34)/2=33Q_3 = (32 + 34) / 2 = 33.
  4. Identify Min and Max Values: Identify the minimum and maximum values. The minimum value is 2424 and the maximum value is 3434.
  5. Construct Box Plot: Construct the box plot using the calculated values.\newlineThe box plot should have a box from Q1Q1 (27)(27) to Q3Q3 (33)(33) with a line at the median (31)(31).\newlineWhiskers should extend from the minimum (24)(24) to the maximum (34)(34).