Question

The data items in a list are 75,86,87,91, and 93. What is the largest integer you can add to the list so that the mean of six items is less than their median?

Answer 1

Largest integer is `101`

Explanation:

There are 5 numbers in the list, but a sixth one is to be added. (as large as possible)

`75" "86" "87" "91" "93" " x`
`color(white)(xxxxxxxxxx)uarr`
The median will be `(87+91)/2 = 89`

Mean will be: `(75+86+87+91+93+x)/6 <89`

`432+x < 6xx89`

`x <534-432`

`x<102`

The largest integer can be 101.

Check; If `x =101`

Mean `= 533/6 = 88.83`

`88.83 < 89`