Problem

Here are the scores of 13 students on a sclence test. \[ 60,62,63,63,70,70,72,73,74,76,80,82,84 \] Notice that the scores are ordered from least to greatest. Glve the median, lower quartlle, and upper quartile for the data set. (a) Median: (b) Lower quartile: (c) Upper quartile:

Solution

Step 1 :Given the scores of 13 students on a science test are: \(60, 62, 63, 63, 70, 70, 72, 73, 74, 76, 80, 82, 84\).

Step 2 :Arrange the scores in ascending order: \(60, 62, 63, 63, 70, 70, 72, 73, 74, 76, 80, 82, 84\).

Step 3 :The median is the middle value of a data set when it is ordered from least to greatest. Since we have 13 data points, the median will be the 7th value, which is \(72\).

Step 4 :The lower quartile (Q1) is the median of the lower half of the data (not including the median if the number of data points is odd). In this case, it will be the median of the first 6 values, which is \(63\).

Step 5 :The upper quartile (Q3) is the median of the upper half of the data (not including the median if the number of data points is odd). In this case, it will be the median of the last 6 values, which is \(78\).

Step 6 :Final Answer: (a) Median: \(\boxed{72}\), (b) Lower quartile: \(\boxed{63}\), (c) Upper quartile: \(\boxed{78}\)

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