Standard Deviation of test scores

In summary, the conversation is about finding the population standard deviation for a class's scores on the Unit 2 mathematics test. The formula for calculating standard deviation is discussed, with one being unbiased and the other biased. The steps for finding the mean and standard deviation are also mentioned, with the correct answers being 79.45 for the mean and 7.54 for the unbiased standard deviation and 7.36 for the biased standard deviation. The conversation ends with the formula being clarified and the correct calculations being made.
  • #1
priscilla98
93
0

Homework Statement



The scores of one class on the Unite 2 mathematics test are shown in the table below. Find the population standard deviation of these scores, to the nearest tenth.

Unit 2 Mathematics Test

Score - Number of people

96 - 1
92 - 2
84 - 5
80 - 3
76 - 6
72 - 3
68 - 2

Homework Equations



standard deviation formula

The Attempt at a Solution



I used this website to find the standard deviation for this problem. But my answer is higher than a 100 and i think i made some miscalculations.
http://www.gcseguide.co.uk/standard_deviation.htm
 
Physics news on Phys.org
  • #2
What you are calculating is unbiased standard deviation. I think you have been asked to calculate biased SD for which the formula is

[tex] \sigma^2 = \overline{(x - \overline{x})^2} [/tex]

For large data sets, you do not have much issues with the two formulae. This difference in formulae is based on biased/unbiased estimators.
 
  • #3
You have to find the mean of the scores first. What did you get?

ehild
 
  • #4
The mean is 79.8095.
 
  • #5
Wouldn't you have to subtract the mean from the test scores?
 
  • #6
Yes, and take the square and the sum of squares. What did you get?

ehild
 
  • #7
in my understanding (please correct if wrong):

mean = (96*1+92*2+84*5+80*3+76*6+72*3+68*2)/sum(people) = 79.45

std deviation = sqrt( sum((score(i)-mean)^2) / (sum(people) - 1)) = 5.57 unbiased
= sqrt( sum((score(i)-mean)^2) / (sum(people))) = 5.44 biased
 
  • #8
The mean is correct, but I got 7.54 and 7.36 for the standard deviations.

ehild
 
  • #9
ehild:
Grateful if you could share the formula please. I am still learning this stuff...
 
  • #10
Your formula is correct. Are you sure you did not make any mistake in the calculation? Did you multiplied the squares with the number they occur? I guess you did not. You have to sum for all people.

ehild
 
Last edited:
  • #11
now I see, indeed haven't multiplied differences squared by number of people. It's the same as your result now.

Thank you!
 

What is the standard deviation of test scores?

The standard deviation of test scores is a measure of the spread or variability of a set of test scores. It tells us how much the scores deviate from the average score.

How is the standard deviation of test scores calculated?

The standard deviation of test scores is calculated by finding the average of the squared differences between each test score and the mean of all the scores. This value is then squared and represents the variance. The square root of the variance is the standard deviation.

Why is the standard deviation of test scores important?

The standard deviation of test scores is important because it provides a more comprehensive understanding of the data. It allows us to see how much the scores vary from the average, and can help identify outliers or extreme scores. It also helps in making comparisons between different sets of test scores.

How does the standard deviation of test scores relate to the normal distribution?

The standard deviation of test scores is closely related to the normal distribution, also known as the bell curve. In a normal distribution, the majority of scores fall within one standard deviation of the mean, with fewer scores falling further away from the mean. This allows us to use the standard deviation to interpret how scores are distributed in relation to the average.

Can the standard deviation of test scores be negative?

No, the standard deviation of test scores cannot be negative. It is always a positive value that represents the amount of variability in the data. A value of zero for the standard deviation means that all the scores are the same, while a higher standard deviation means that the scores are more spread out.

Similar threads

Determine the standard deviation of these results
    • Precalculus Mathematics Homework Help
Replies
10
Views
2K
Finding ∑fx and ∑fx^2 from the standard deviation and mean
    • Precalculus Mathematics Homework Help
Replies
4
Views
11K
Stats 1 question: standard deviation
    • Precalculus Mathematics Homework Help
Replies
1
Views
2K
Calculations using Standard Deviation and Mean
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Testing of the hypothesis of variance
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
MHB Standard deviation, raw score etc
    • General Math
Replies
1
Views
2K
MHB Does the entrance test score determine the final exam score?
    • General Math
Replies
3
Views
1K
Calculate the bulk modulus and Derive the mean standard deviation
    • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
I What is the significance of standard deviation for arbitrary distributions?
    • General Math
Replies
4
Views
1K
A Low value standard deviation bias
    • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top