The median, mode , and mean of a data is 9, if there are five integers in the data and the range of the data is 4. If the least value of the data is 7, then find the number of different observations in the data.

Options

A. 3
B. 4
C. 2
D. 5

Answer

A

Explanation

There are five integers in the data.
given mode `=9`
`:.` There must be at least two 9' s.
Also given that the least value is 7 and range is 4.
`:.` The greatest value is 11.
`:.` 7, 9, 9, are 11 are the four observation of the data.
Let the 5th observation be x.
Since mean is 9, the sum of the observations must be 45.
`:. 45-(7+9+9+11)=x`
`45-(36)=x`
`:. x=9`
`:.` Number of different observations in the data is 3.
Hence, the correct option is (a).