Question

On the first 7 statistics tests of the semester, scored 61, 76, 79, 80, 80, 84, and 91. The mean,

median, and mode of his scores were 79, 80, and 80,

respectively. On the 8th statistics test, Jamal scored 90. How do the mean, median, and mode of all 8 of his )

scores compare to the mean, median, and mode of his

first 7 scores?

Answer 1

Well in terms of mean it would undoubtedly raise it. Because it takes into account all values it can sometimes be more accurate but it can also fall prey to high outliers, so even adding on value that is way to the left or right can influence the result.
The median will not be affected. Because it is the middle value. So the fourth value(count values from 61,91 with 61 being 1) is 80 which is the middle one. While with 8 data points, it would be the 4th + 5th both divided by 2. However (80 + 80)/2 is 80. So median is unchanged.

Now for the mode. Remember the mode is the most common number. Because 90 does not match another value, 80 is still the most common value which means it remains unchanged. (This is why mode is often the most useless measurement unless you have a lot of data points)