math help please?

Question

The following scores were recorded on a 100-point examination:
91, 85, 76, 86, 96, 51, 68, 92, 85, 72, 66, 88, 93, 82, 84

(a) Find the mean final examination score.
(b) Find the median final examination score.
(c) Is the mean or median a more useful representative of the final examination scores?


can someone help me with this.. I think i picked the right one but want to see if anyone else has also to make sure i am right.

thanks

Answer 1

As mentioned above, the mean is sum/15 = 81. The median is the 8th smallest number, which is 85.
However, the most important one is question c), to which the answer is most definitely 'median'.
It is not as apparent in this example, but consider what would happen if you had 10 people sit an exam. Nine of them got 90, and one of them got 0. The mean would be 81, but the median would be 90.
With exam marks like this, you *always* use the median. Half of people will get less; half of people will get more, and it is not affected by very high or very low scores (of which there are always in any exam.)

Answer 2

a) Add all the terms together, then divide by the total number of terms: 1215/15 = 81

b) Put terms in chronological order, then pick whichever one falls in the middle:
51, 66, 68, 72, 76, 82, 84, _85_, 85, 86, 88, 91, 92, 93, 96
85 is the eighth, or median, term.

c) This is an opinion question. Usually, in "how are people doing" questions, the median is used because it tells you where the middle guy ended up, and it's not skewed by exorbitantly low or high readings. For example, when economists report income data as a measure of national economic health, they don't give the mean income, because that is easily thrown off by the Bill Gateses of the country. They instead report the median income, which is the income at which 50% of the people are richer and 50% are poorer.

Answer 3

(a) Mean is average. So if you add them all up (total is 1215) and then divide by 15 (15 tests total) then you get 81.

(b) The Median is the middle number when the numbers are listed in order from smallest to largest.
51, 66, 68, 72, 76, 82, 84, 85, 85, 86, 88, 91, 92, 93, 96
The middle number is 85.

(c) The mean is more useful, because it tells you the average score of the whole class, and the median only tells you what the middle person got on the test, which isn't very relevant.

Answer 4

First you have to write this in a new line starting with lowest left and ending with the highest on the right: 51, 66, .... 93,96.

There are 15 numbers and median means thee number in the center: 15 divided by 2 is 7.5, so the 8th number is the median.

To find the mean you have to add all 15 numbers and divide by 15.

What is better: thee is no clear answer. If you are the person with the score for number 8 you know that they were 7 people worse than you and 7 people better than you.

The calculation of the mean number is just a theoretical number, i assume in this case it is also a broken number as e.g. 78,3457443.

I In some cases the median has more meaning e.g when you count discrete things (e.g when you form a line of people smallest to largest, sometimes the other makes more sense e.g. when you want to find out what the average price of a product is (you have offers from 10 companies for a car and want to know the average market price).

I hope this helped .....

Answer 5

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Answer 6

a) mean= average, (#+#+#.....)divided by number of numbers, 81
b) median=order them from least to greatest; the middle number, 85
c) mean

Answer 7

a) 81
b) 92
c) mean

Answer 8

a.)81
b.)85
c.)mean