Question

A set of data that shows temperature highs for 10 days and satisfies all conditions below mean:72 median:74 mode:68 range:21

Answer 1

`58, 68, 68, 68, 74, 74, 76, 77, 78, 79`

Explanation:

Given

`n=10`

`Mean = 72`

`Median = 74`

`Mode = 68`

`Range = 21`

Required

The complete dataset

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From the mean, we have:

`Mean = (\sum x)/(n)`

This gives:

`72 = (\sum x)/(10)`

Cross multiply

`\sum x = 72 * 10`

`\sum x = 720`

This means that the sum of all elements of the dataset is 720

Next, we test the median

Since n = 10, then:

`Median = (n + 1)/(2)`

`Median = (10 + 1)/(2)`

`Median = (11)/(2)`

`Median = 5.5th`

This implies that the median is the average of the 5th and 6th item.

So, we have:

`Median = (5th + 6th)/(2)`

Cross multiply

`5th + 6th = 2 * Median`

`5th + 6th = 2 * 74`

`5th + 6th = 148`

This means that the 5th and 6th element add up to 148

Also, we have:

`Mode = 68`

This means that 68 has to appear at least twice in the dataset

`Range = 21`

This implies that the difference between the highest and the least is 21.

The dataset that satisfies the above condition is:

`58, 68, 68, 68, 74, 74, 76, 77, 78, 79`