Question

The range of the cards is 6, the median of the cards is 7, the mean of the cards is 8, work out the missing numbers

Answer 1

Question:

There are 5 cards in order from smallest to largest, 5 _ _ _ _. The range of the cards is 6, the median of the cards is 7, the mean of the cards is 8, work out the missing numbers

Answer:

5, 6, 7, 11, 11 or 5, 7, 7, 10, 11

Explanation:

Given

`Range = 6`

`Median = 7`

`Mean = 8`

Required

Complete the blanks

Range is calculated as:

`Range = Highest - Lowest`

From the given numbers, we have:

`Range = 6`

`Lowest = 5`

So, the equation becomes

`6 = Highest - 5`

`Highest = 5 + 6 = 11`

So, we have:

5 _ _ _ 11

Next,

`Median = 7` means that the middle number is 7;

So, we have:

5 _ 7 _ 11

Next,

`Mean = 8`

Let the two remaining blanks be x and y: 5 x 7 y 11

Where

`5 \le x \le 7` and
`7 \le y \le 11`

So, we have:

`(5 + x + 7 + y + 11)/(5) = 8`

Collect like terms

`(5 + 7+11+ x + y )/(5) = 8`

`(23+ x + y )/(5) = 8`

Cross Multiply

`23 + x + y = 8 * 5`

`23 + x + y = 40`

`x + y = 40 - 23`

`x + y = 17`

Recall that:
`5 \le x \le 7` and
`7 \le y \le 11`

Using trial by error, we have:

`x + y = 17`

`6 + 11 = 17`

`x = 6\ and \ y = 11`

`7 + 10 = 17`

`x = 7\ and \ y = 10\\`

Hence, the complete cards could be: 5, 6, 7, 11, 11 or 5, 7, 7, 10, 11