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In the data set below, what are the lower quartile, the median, and the upper quartile?\newline21,47,48,54,60,7421, 47, 48, 54, 60, 74\newlinelower quartile==____\_\_\_\_\newlinemedian==____\_\_\_\_\newlineupper quartile==____\_\_\_\_

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Q. In the data set below, what are the lower quartile, the median, and the upper quartile?\newline21,47,48,54,60,7421, 47, 48, 54, 60, 74\newlinelower quartile==____\_\_\_\_\newlinemedian==____\_\_\_\_\newlineupper quartile==____\_\_\_\_
  1. Question Prompt: Question prompt: Determine the lower quartile, median, and upper quartile for the given data set: 21,47,48,54,60,7421, 47, 48, 54, 60, 74.
  2. Arrange Data Set: Arrange the data set in ascending order, if it is not already. The given data set is already in ascending order: 21,47,48,54,60,7421, 47, 48, 54, 60, 74.
  3. Find Median: Find the median of the data set. Since there are an even number of observations (66 numbers), the median will be the average of the middle two numbers. The middle two numbers are 5454 and 6060. \newlineMedian calculation: (54+60)/2=114/2=57(54 + 60) / 2 = 114 / 2 = 57\newlineMedian: 5757
  4. Identify Lower Quartile: Identify the data set for the lower quartile. For the lower quartile, consider the first half of the data set, excluding the median if it is a number in the data set. Since we have an even number of observations, we will take the lower three numbers: 2121, 4747, 4848.
  5. Find Lower Quartile: Find the value of the lower quartile. Since there are 33 numbers in the lower half, the lower quartile will be the middle number of these three.\newlineLower quartile: 4747
  6. Identify Upper Quartile: Identify the data set for the upper quartile. For the upper quartile, consider the second half of the data set, excluding the median if it is a number in the data set. The second half is 5454, 6060, 7474.
  7. Find Upper Quartile: Find the value of the upper quartile. Since there are three numbers in the upper half, the upper quartile will be the middle number of these three.\newlineUpper quartile: 6060

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