Mean,median,mode

Question

in the mathematics class half of the students scored 92 on an achievement test . with the exception of a few students who scored 54 the remaining students scored 73 . which of the following statements is true about the distribution of scores?

A. The mean is greater than the median

B. The mean and the median are the same

C. The mean is greater than the mode

D. The mean is less than the median

Answer 1

To solve this problem we need to understand the definition of "median," which is the middle number in a set of data. It's the number for which: half the data is larger and half the data is smaller.

To help us visualize let's assume this class only has 8 students. We know that half of them scored a 92, a "few" scored a 54, and the "rest" a 73. You can do this with any data set that aligns with the information we have on the classroom, but for our sake let's assume the data looks like this:

54 54 73 73 92 92 92 92

Here, we can quickly see that the median is somewhere between 73 and 92 (82.5 to be exact).

We can also see that the mean is being pulled down by the few students who scored a 52. In our make believe classroom the mean is ( 54 + 54 + 73 + 73 + 92 + 92 + 92 + 92 ) / 8 = 77.75.

This proves that D. The mean is less than the median

You can reach the same conclusion with any set of data. For example, for a class of 15, represented below:

54 54 73 73 73 73 73 92 92 92 92 92 92 92 92

Median: 92

Mean: 80.6