A set of data has a mean of 16

grislingatb

grislingatb

Answered question

2021-11-26

Which of the following numbers must correspond to a value in the data set where the mean, median, and mode are all 16, 15, and 14?

Answer & Explanation

huckelig75

huckelig75

Beginner2021-11-27Added 11 answers

Step 1
We know that, Mean value of a dataset is the average value of a dataset which is generally not lie in the dataset. For example, let us take dataset as 2,3,4,3,5,6 then you obtain the mean value as 3.83 which is not a value of the dataset.
Again, Median value may not lies in the dataset sometimes because, for even number of observation, Median is the average is the mean of two middle terms. For example, the Median of the above dataset is 3+42=3.5 which is not a value of the dataset.
But Mode is the value which has maximum occurrence in the dataset. There is no need for any calculation for mode. For example, Mode of the above dataset is 3 which is one of the values of in dataset.
Step 2
Thus, if a dataset has a mean of 16 and a median of 15 and a mode of 14. Then,
Mode =14 must be a value in the dataset.

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