The mean of a data set is 7.8, the mode is 6.6, and the median is 6.8. what is the least possible number of data values in the set?
a. 3 data values
b. 4 data values
c. 5 data values
d. 6 data values

Option C - The minimum number of data values in the set is 5.

Step-by-step explanation:

Given : The mean of a data set is 7.8, the mode is 6.6, and the median is 6.8.

To find : What is the least possible number of data values in the set?

Solution :

By the definitions of the statistical measures,

Mean = (Sum of all data)/Number of data,

Mode is the most frequently occurring actual value,

Median is the value midway between the highest and lowest values in the data set.  Md – L = H – Md.

Now, We have given,

Mode = 6.6 = actual value

6.8 is the higher value as it cannot be the lowest value because then the highest would be less than the mean.

A minimum real number of 0 makes the upper limit 13.6 for a median of 6.8.

So,  

With a minimum of 2 '6.6' values for a mode, each other number must be unique.

With a lower value of '0', an upper value of '13.6', and a mean of 7.8.

Our data set is [0, 6.6, 6.6, x, 13.6].

The 'x' calculates out to 12.2 to satisfy the conditions stated.

Therefore, The minimum number of data values in the set is 5.

So, Option C is correct.

7,24

step-by-step explanation: