Question

The mean of a data set is 7.8. The mode is 6.6 in the median is 6.8 what is the least possible number of data values in the set?

Answer 1

Since the mode is 6.6, there must be at least one data value that is 6.6 in the set. Similarly, since the median is 6.8, there must be at least one data value that is 6.8 in the set.

Let's assume that there are only two data values in the set: 6.6 and 6.8. The mean of these two values is (6.6+6.8)/2 = 6.7, which is not equal to the given mean of 7.8. Therefore, there must be at least one more value in the set that is greater than 6.8.

Let's assume this third value is x. Then, we know that:

(6.6 + 6.8 + x)/3 = 7.8

Multiplying both sides by 3, we get:

6.6 + 6.8 + x = 23.4

x = 10

So we have three data values: 6.6, 6.8, and 10.

Therefore, the least possible number of data values in the set is three.