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
Can someone explain how I am supposed to solve this?
To determine the minimum number of data values in the set, we need to consider the relationship between the mean, mode, and median.
Mean: The mean is the average of all the data values. In this case, the mean is given as 7.8.
Mode: The mode is the value that appears most frequently in the data set. Here, the mode is given as 6.6.
Median: The median is the middle value when the data set is arranged in increasing or decreasing order. The median here is given as 6.8.
To determine the minimum number of data values, we need to consider the relationship between these statistics.
Since the mode is given as 6.6, at least one data value must be 6.6. The median is given as 6.8, so at least one data value must be 6.8.
Now, let's consider the mean. The mean is found by adding up all the data values and dividing by the total number of values. In this case, the mean is given as 7.8.
Since the two known data values (6.6 and 6.8) are both less than the mean (7.8), it means that the remaining data values must be greater than the mean to make the average equal to 7.8.
So, starting with the minimum number of data values, we can eliminate option A (3 data values) because having only three data values (6.6, 6.8, and another value greater than 7.8) would result in a mean higher than 7.8.
Similarly, we can eliminate option B (4 data values) because adding another data value greater than 7.8 would still result in a mean higher than 7.8.
Therefore, the minimum number of data values needed to achieve a mean of 7.8 is option C (5 data values). This would give you a set of values, including 6.6, 6.8, and three more values greater than 7.8, which would balance out the mean to be 7.8.
So, the correct answer is C. 5 data values.