Question

For a particular sample of 58 scores on a psychology exam, the following results were obtained.
First quartile = 52 Third quartile = 84 Standard deviation = 10 Range = 66
Mean = 79 Median = 78 Mode = 81 Midrange = 65
Answer each of the following:
I. What score was earned by more students than any other score? Why?
II. What was the highest score earned on the exam?
III. What was the lowest score earned on the exam?
IV. According to Chebyshev's Theorem, how many students scored between 59 and 99?
V. Assume that the distribution is normal. Based on the Emp

Answer 1

The first one is easy, right?

Answer 2

yes

Answer 3

Now, http://en.wikipedia.org/wiki/Mid-range

Answer 4

thanks

Answer 5

So the top score is half the range above the midrange and the bottom score is half the range below the midrange. Yes?

Answer 6

i 'm not sure

Answer 7

http://en.wikipedia.org/wiki/Chebyshev%27s_inequality

the precise statement being that no more than 1/k^2 of the distribution’s values can be more than k standard deviations away from the mean.

Answer 8

We'll go back to Chebyshev. The midrange is by definition the average of the top and bottom scores.

Answer 9

OK with that?

Answer 10

yes

Answer 11

Back now

Answer 12

So we have top and bottom scores and the midrange is half way in between, so half the range is above it and half below.

Answer 13

Now back to Chebyshev. You'll notice in part IV they ask about the scores between 59 and 99, that is, between 2 SD below the mean and 2 SD above it. OK?

Answer 14

So Chebyshev says
no more than 1/k^2 of the distribution’s values can be more than k standard deviations away from the mean.
We're looking at k = 2
So he'd say that no more than 1/4 of the scores are outside the range 59-99 and therefore 3/4 must be inside that range.

Answer 15

OK with that?

Answer 16

ok

Answer 17

What's the last question? I can't quite make it out.

Answer 18

Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 69 and 89?