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?
1 Answer
5
Explanation:
From the definitions of the statistical measures, Mean = (Sum of all data)/Number of data, Mode is the most frequently occurring actual value, and the Median is the value midway between the highest and lowest values in the data set. Md – L = H – Md.
6.6 is an actual value. 6.8 is higher, so the highest value must be higher yet. 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.
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, we have only one more value with which to adjust the mean. Our data set is [0, 6.6, 6.6, x, 13.6]. The 'x' calculates out to 12.2 to satisfy the conditions stated. Thus, the minimum number of data values in the set is 5.
If you would like a physically real value for the minimum (1), then the upper value must be 14.6 and the adjustable value becomes 10.2, but the number of values in the data set remains a minimum of 5.
