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Find the median and mean of the data set below:

47, comma, 15, comma, 6, comma, 49, comma, 45, comma, 30
47,15,6,49,45,30

1 answer

To find the median and mean of the data set \(47, 15, 6, 49, 45, 30\), we can follow these steps.

Step 1: Calculate the Mean

The mean (average) is calculated by summing all the values and dividing by the number of values.

  1. Sum the values: \[ 47 + 15 + 6 + 49 + 45 + 30 = 192 \]

  2. Count the number of values: There are 6 values in the data set.

  3. Calculate the mean: \[ \text{Mean} = \frac{192}{6} = 32 \]

Step 2: Calculate the Median

The median is the middle value when the data set is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.

  1. Order the data set: \[ 6, 15, 30, 45, 47, 49 \]

  2. Find the middle values: Since there are 6 values (an even number), the median will be the average of the 3rd and 4th values in the ordered list:

    • 3rd value: 30
    • 4th value: 45

  3. Calculate the median: \[ \text{Median} = \frac{30 + 45}{2} = \frac{75}{2} = 37.5 \]

Summary

  • Mean: \(32\)
  • Median: \(37.5\)