Z-score Question (1 Viewer)

[HasiiM]

Hello i am having a problem with this question. I have got the correct mean and sd required but cannot figure the z-score.

Question

Tests were held in Maths and English and the mark for 10 students are recorded below :

MATHS : 67 70 82 75 68 88 78 71 88 86

ENGLISH: 68 86 76 84 74 72 90 84 62 53

A) Find the mean and Standard deviation of the maths marks!

X = 77.3
SD = 7.86

B) Find the mean and the standard deviation of the english marks!

X = 74.9
SD = 11.05

My problem begins here...

C) Kelly scored 76 in English, Find the Z-Score corresponding to this mark.
( Im getting a score of like 0.09....but i know its not correct )

D) Kelly scored 78 in Maths. Which was the better result?!

Thanks in advance

 

[Drongoski]

If I've not forgotten my stats:




Therefore a score of 76 in English is a better result than 78 in maths since 0.0995 ... > 0.08905 ...

 

[HasiiM]

Yes i have also gotten those stats, but i have asked my teacher on this question and told me to check them again, i didn't think i was wrong.

 

[PC]

I think you may have found the SAMPLE deviation (s_n-1) instead of STANDARD deviation (s_n).

I get the following stats:
Maths (mean = 77.3, standard deviation = 8.3)
English (mean = 74.9, standard deviation = 11.6)

Then I usually draw up a quick number line to see if that will solve the problem, but both these scores are between 0 and 1 standard deviations from the mean. So we have to use the formula.

For Maths:
z = (78 – 77.3)/8.3 = 0.084

For English:
z = (76 – 74.9)/11.6 = 0.094

So the mark in English is better.

 

[Kat92]

@PC is right.

I think that you may have found the population standard deviation x row n instead of the sample standard deviation x row n ^-1. You need to use the sample standard deviation as it states only 10 students out of the class were selected.

A) Maths:
Mean = 77.3
sample standard deviation= 8.3.

B)English:
Mean=74.9
sample standard deviation=11.6

C) English
z= x- x bar/ s
z=76-74.9/ 11.6
z= 0.095

D) Maths
z=x- x bar/ s
z= 78-77.3/ 8.3
z=0.084

Therefore Kelly performed better in English due to the higher z-score.

If the question was talking about a scenario of golf for example a lower z-score would be more beneficial.

Also remember z-scores must be between -3 and +3 nothing more or less otherwise there is a mistake in your calculation!

 

[PC]

Also remember z-scores must be between -3 and +3 nothing more or less otherwise there is a mistake in your calculation!

Actually, it's possible to get z-scores higher than 3, but it's just very unlikely. Remember that only 99.7% of scores are within 3 standard deviations from the mean, so there are still others with higher z-scores.

 

[Kat92]

Very true, I kind of forgot to mention that. It is very evident especially for when you are comparing z-scores in a normal distribution curve for different events.

 

[MzBiiBii]

my teacher told us to always use the sample deviation, rather than standard deviation..sometimes it works and sometimes it doesnt ..

What's the difference between them?

 

[timw7845]

my teacher told us to always use the sample deviation, rather than standard deviation..sometimes it works and sometimes it doesnt ..

What's the difference between them?

you use the standard deviation...

sample is a few randoms picked out of a group of people

 

[Uncle]

oh my god first two week of ninjaneering statistics