# Thread: Standard Deviation. No idea!

1. ## Standard Deviation. No idea!

I've got to hand this in for tomorrow. No problems. But I can't do standard deviation!

It's these online worksheets, and the teacher expects them to be done. I have tried my hardest to work it out revision guides, etc. No help

There are four questions:

1) A teacher records results on the length of time taken to do a test:
24, 18, 21, 17, 25, 19, 23, 17, 25, 15
Find the mean: Find the S.D

Once they have completed the test, each pupil sits a mental arithmetic test, which takes 5 mins.
Write the New Mean Write the new S.D

2) 23 archers take part in a competition, they get a score out of 600. The sum of their scores is 11 362 the sum of the squares of the scores is 5645713
Find the mean: Find the S.D

One archer's score is incorrectly recorded as 341. He actually scored 346
Find the new mean Find the new S.D

3) Afolabi goes swimming twice a week. He records how many lengths he swims each time here are the results

Lengths Frequency
20 5
22 9
24 19
26 28
28 26
30 13

Find the mean length Find the S.D.

The next time he goes swimming he does 9 lengths. How does this affect the S.D? Increase. Decrease. Can't tell

4) A teacher asks her closs how long they spend doing their homework.

Time Freq
0<t<=10 1
10<t<=20 3
20<t<=30 6
30<t<=40 16
40<t<=50 2
50<t<=60 2

Find the mean. Find the S.D

A student was absent when the results were recorded. She spent from 30-40mins doing her homework

Find the new mean Find the new S.D

2. Let's start with problem #1, which will give you a underlying knowledge for the other problems.

You have a number set of time scores as follows:

24, 18, 21, 17, 25, 19, 23, 17, 25, 15

To get standard deviation, you need variance, to get variance, you need mean. Go here, and enter your number set:

Mean, Variance, and Standard Deviation

Follow the math to see how to calculate mean, variance, and standard deviation.

Then we can move on to the other problems.

3. I see. You subtract the mean from the number, then square it.

Add them up, over the number of them and then - the mean 2

It's the more complicated things I think I'm going to have problems with. Not least that I don't understand the question.

Thanks for your help so far!

4. Originally Posted by sam93
I see. You subtract the mean from the number, then square it.

Add them up, over the number of them and then - the mean 2

It's the more complicated things I think I'm going to have problems with. Not least that I don't understand the question.

Thanks for your help so far!
Yes, the mean is the average of your number set.

The variance is the squared differences of each number in the number set minus the mean. All of that is divided by the number of entries in your number set, in this case, 10.

Standard Deviation is the Square Root of Variance.

6. I'm confused at the 2nd part of your 1st question, I think you are trying to say that each of them add 5 minutes to their time scores. Is that correct? If so, repeat the same step I showed you by hand first, before you use my calcuator here. Use the calculator to check your answers.

Then we can move on.

7. To be quite honest, I am not sure myself, I just copied out what the question said. I will try it and see if it works (its an instant marking thing)

8. Originally Posted by sam93
To be quite honest, I am not sure myself, I just copied out what the question said. I will try it and see if it works (its an instant marking thing)
Problem 2:

2) 23 archers take part in a competition, they get a score out of 600. The sum of their scores is 11 362 the sum of the squares of the scores is 5645713
Find the mean: Find the S.D

Since their total score is 11362, and we know we have 23 archers, our mean is 11,362/20. Can you follow from here to get SD?

9. Mean: 25.4
Standard Deviation: 3.50

To three S.F

I marked it, and it was correct.

10. Originally Posted by sam93
Mean: 25.4
Standard Deviation: 3.50

To three S.F

I marked it, and it was correct.

Problem 3 is the same as Problem 1. Your number set is your lengths, ignore frequency.

Find mean, variance, and Standard Deviation.

11. I doubt you teacher want this in tomorrow that badly seeing that it is a public holiday in Britain.

Firstly you should be familiar with the formula. for standard deviation, which is.

$\displaystyle \sigma = \sqrt{ \frac {\sum x^2}{n} - \mu^2 }$

where $\displaystyle \mu$ is the population mean.

Next you draw out a table like this.

$\displaystyle \left.\begin{array}{c|c|c|c|c|c|c|c|c|c|c} x & 24 & 18 & 21 & 17 & 25 & 19 & 23 & 17 & 25 & 15 \\\hline x^2 & 576 & 324 & ? & ? & ? & ? & ? & ? & ? & ?\end{array}\right.$

I will let you fill in the blanks.

Note $\displaystyle \mu = \frac{\sum x}{n} = \frac{24 + 18 + 21 + 17 .... + 25 + 15}{10}$

then $\displaystyle \frac {\sum x^2}{n} = \frac {567 +324 + ..}{10}$

and then you use the formula to calculate the standard deviation.

Bobak

12. ..23 archers :-)

This is actually the bit I get confused on, becuase I dont have the raw data.

Could you work through with me, to see if I can understand

13. Post 4, part 1, you'd do the same thing, using the frequencies as your number set.

Post 4, part 2, you'd add one to the entry of the time frequency the problem specifies, and recalculate the mean, variance, and standard deviation.