You are Here: Home >< Maths

# Which one of the following has the highest standard deviation and why? Watch

1. Mean +/- Standard Deviation.

1) 24 +/- 12
2) 57 +/- 17
3) 150 +/- 68
4) 22 +/- 15

is it 3?

if so, then using the formula SD/ Mean * 100.

why does option 4 give you the highest %.

15/22 *100 gives you 68%
2. Strange notation to present the data but from what it says then yes, it is 3 because the standard deviation is 68 instead of 15 in comparison to 4).
The fact the 4) gives you the highest % according to your formula simply tells you that as a proportion of the mean the data in 4) is more spread, but standard deviation is simply a measure of spread from the mean, not as a proportion of it.

For example, the data sets
0,1,1,3,4,9 and 1000,1001,1001,1003,1004,10009 have the same standard deviation because they are spread in the same way around their respective means.
3. (Original post by bcrazy)
Strange notation to present the data but from what it says then yes, it is 3 because the standard deviation is 68 instead of 15 in comparison to 4).
The fact the 4) gives you the highest % according to your formula simply tells you that as a proportion of the mean the data in 4) is more spread, but standard deviation is simply a measure of spread from the mean, not as a proportion of it.

For example, the data sets
0,1,1,3,4,9 and 1000,1001,1001,1003,1004,10009 have the same standard deviation because they are spread in the same way around their respective means.
Thank you!!!! and why did you say it's a strange notation?

I thought the ' +/-' sign is the the standard notation, since it shows how the standard deviation varies about the mean.
also why is 4 more spread out? I thought the greater the standard deviation, the greater the spread.
4. (Original post by CyberKid)
Thank you!!!! and why did you say it's a strange notation?

I thought the ' +/-' sign is the the standard notation, since it shows how the standard deviation varies about the mean.
also why is 4 more spread out? I thought the greater the standard deviation, the greater the spread.
Suppose the notation makes some sense- just personally don't think I've ever seen it written like that before during 4 years of a Stats degree.

And sorry...wasn't claiming 4) was more spread, was just saying that as a proportion of the mark it was more spread- which can be useful to consider in some cases:

For example, consider two tests- Test 1 is marked out of 10 and Test 2 is marked out of 100.
Results from Test 1: 6,8,4,9,2,10
Results from Test 2: 83,81,79,90,95,88

The standard deviation is bigger for Test 2 and therefore our conclusion would be that the results in Test 2 are more spread, which objectively they are.
However, when considered in context we can clearly see that the results in Test 1 are less "consistent" when considered as percentages of the possible mark. Therefore comparing standard deviation to talk about spread is only really valid when the population from which your two sets of data are coming from are comparable.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 29, 2010
Today on TSR

### Cambridge interview invitations

Has yours come through yet?

### Official Oxford interview invite list

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.