Here is a list of eight whole numbers.8 19 14 15 23 6 4 xThe median of these eight numbers is 12.(a) Find the value of x .(b) Calculate the mean of the eight numbers.
Question
Here is a list of eight whole numbers.8 19 14 15 23 6 4 xThe median of these eight numbers is 12.(a) Find the value of x .(b) Calculate the mean of the eight numbers.
Solution
(a) The median is the middle number in a sorted list of numbers. In a list of 8 numbers, the median is the average of the 4th and 5th numbers. Given that the median is 12, the 4th and 5th numbers must add up to 24. If we sort the given numbers, we get 4, 6, 8, 14, 15, 19, 23, and x. The 4th number is 14 and the 5th number is 15, which add up to 29. This is more than 24, so x must be less than 14. If we place x as the 4th number, the 4th and 5th numbers add up to 14 + x = 24. Solving for x, we get x = 10.
(b) The mean is the sum of all numbers divided by the count of numbers. Adding all the numbers including x, we get 4 + 6 + 8 + 10 + 14 + 15 + 19 + 23 = 99. Dividing by 8, we get the mean as 99 / 8 = 12.375.
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