Answer:
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.
