Question

Create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.

Step 1:
What thought process did you use to create your numbers?

a Choose five numbers with a mean of 10. Next adjust the numbers to have a standard deviation of 3. This will automatically ensure that the median is 10 − 3 = 7.
b First choose 5 numbers that have a median of 7, such as (5,6,7,9,10). Next adjust the highest number so that the mean will be 10. This must be done so that it still remains the highest number.
c Start by choosing 5 ordered numbers so that the middle one is 7. Next adjust the other numbers so that the mean is 10 without changing the ordering of the numbers.
d It is impossible to choose 5 numbers that satisfy this condition.

Answer 1

Explanation:

Two cases arise to obtain the median.

Case (1): Sample size (n) is odd

First, arrange the data in ascending order. Then, the median is the middle value and lies at the
`{\left( {\frac{{n + 1}}{2}} \right)^{{\rm{th}}}}` position.

Case (2): Sample size (n) is even

First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on and positions.

Formula for mean is, where is the sum of all observations and n is the total number of observations.

(1)

Use the below process to create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.

1.Select the 5 ordered numbers with middle value 7.

2.Adjust the remaining 4 numbers other than 7 to get mean 10 without changing the order of the numbers.

Based on the process to select the 5 ordered numbers with middle value 7 and change the other ordered numbers to get the mean value 10.

(2)

The product of the mean and the total number of observations is obtained. Then, the sum of four observations is subtracted from the product.

Here, the first four numbers are (5, 6, 7, 8).

The last number by using mean 10 is,

`\begin{array}{c}\\\bar x = \frac{{5 + 6 + 7 + 8 + a}}{5}\\\\10 = \frac{{5 + 6 + 7 + 8 + a}}{5}\\\\50 = 26 + a\\\\a = 50 - 26\\=24\end{array}`

The last number is 24.