Question

please help?
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. Bas

Answer 1

I. Mode = # occurring most often (could be more than one number)

Answer 2

is there any way to tell for sure?

Answer 3

For I ?? It is the definition of "mode".

Answer 4

http://www.purplemath.com/modules/meanmode.htm

Answer 5

ohh ok. That makes sense. I just wasn't sure because for the mode there was no way of telling which number occured more often.

Answer 6

the problem tells you which score occurred most often: Mode = 81

Answer 7

ohh ok. I really got tripped up and started to over analyze. Thank you

Answer 8

for the highest answers, do we use the mean?

Answer 9

not sure, I'm thinking about it...

Answer 10

ok. Thank you

Answer 11

highest score is 98.

Answer 12

I used the mid-range and the range to find it.

Answer 13

what do you mean? Adding them together?

Answer 14

Let H = highest score
Let L = lowest score

Midrange = \(\large \dfrac{H +L}{2}\)
and
Range = \(\large H-L\)

Answer 15

ohh! ok!

Answer 16

we know that \(H-L = 66\) so \( L = H - 66\). We also know that \( \dfrac{H +L}{2} = 65\) so substituting \(H - 66\) for \(L\) we get
\[ \frac{H+H-66}{2} = 65\]
\[\frac{2H - 66}{2} = 65\]
\[2H-66 = 130\]
\[2H = 196\]
\[H = 98\]

Answer 17

2H would be 2*H, right?

Answer 18

Right, 2H means 2 times H.

Answer 19

that is awesome. Thank you tons for helping me. It's very tricky

Answer 20

yah, I wasn't sure how to get that at first...

Answer 21

you're a lifesaver :D

Answer 22

lol :)

Answer 23

how about that last question?