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In the data set below, what are the lower quartile, the median, and the upper quartile?\newline58,63,66,70,72,9458, 63, 66, 70, 72, 94\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?\newline58,63,66,70,72,9458, 63, 66, 70, 72, 94\newlinelower quartile==__\_\_\newlinemedian==__\_\_\newlineupper quartile==__\_\_
  1. Arrange Data Set: Arrange the data set in ascending order if it is not already sorted.\newlineThe given data set is already in ascending order: 58,63,66,70,72,9458, 63, 66, 70, 72, 94.
  2. Find Median: Find the median of the data set.\newlineSince there are 66 numbers, the median will be the average of the 33rd and 44th numbers.\newlineMedian =(66+70)/2=136/2=68= (66 + 70) / 2 = 136 / 2 = 68.
  3. Identify Lower Quartile: Identify the data set for the lower quartile.\newlineFor the lower quartile, consider the first half of the data set, excluding the median if it is a single number. Since we have an even number of observations, we include both the 3rd3^{\text{rd}} and 4th4^{\text{th}} numbers.\newlineFirst half is 5858, 6363, 6666.
  4. Find Lower Quartile: Find the value of the lower quartile. The lower quartile is the median of the first half of the data set. Since there are 33 numbers, the lower quartile is the middle number, which is 6363.
  5. Identify Upper Quartile: Identify the data set for the upper quartile.\newlineFor the upper quartile, consider the second half of the data set, excluding the median if it is a single number. Since we have an even number of observations, we include both the 3rd3^{\text{rd}} and 4th4^{\text{th}} numbers.\newlineSecond half is 7070, 7272, 9494.
  6. Find Upper Quartile: Find the value of the upper quartile. The upper quartile is the median of the second half of the data set. Since there are 33 numbers, the upper quartile is the middle number, which is 7272.

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