Stats 1 question: standard deviation

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  • #1
I missed the lesson on this and i can't figure out how to do this question with the data given.

Homework Statement



A class of 20 students takes a test. The score, x , for each student was recorded by the teacher. The results of summarised by:
∑(x-10) = 208 and ∑(x-10)² = 2716

i) calculate the standard deviation of the 20 scores.
ii)show that ∑x² = 8876
iii) Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.

Homework Equations



unsure

The Attempt at a Solution



I tried i, ∑(x-10)² / 20 =varience = 2716/20
standard deviation =√(2716/20)= 11.65
I think this is wrong though because 10 isn't the mean.
 
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  • #2
whitefeather said:
I missed the lesson on this and i can't figure out how to do this question with the data given.

Homework Statement



A class of 20 students takes a test. The score, x , for each student was recorded by the teacher. The results of summarised by:
∑(x-10) = 208 and ∑(x-10)² = 2716

i) calculate the standard deviation of the 20 scores.
ii)show that ∑x² = 8876
iii) Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.

Homework Equations



unsure

The Attempt at a Solution



I tried i, ∑(x-10)² / 20 =varience = 2716/20
standard deviation =√(2716/20)= 11.65
I think this is wrong though because 10 isn't the mean.

So, you need to find the mean. Alternatively, you can just look at y = x-10 instead of x. How are the variance of x and the variance of y related?

RGV
 

1. What is standard deviation and how is it calculated?

Standard deviation is a measure of how much the data values deviate or vary from the average. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

2. Why is standard deviation important in statistics?

Standard deviation is important because it provides a measure of the spread of the data. It helps us understand how much the data values differ from the average and allows us to make comparisons between different sets of data.

3. How does the standard deviation change with different data sets?

The standard deviation can change depending on the data set. If the data values are spread out, the standard deviation will be larger, and if the data values are close together, the standard deviation will be smaller.

4. What is a high or low standard deviation?

A high standard deviation means that the data values are more spread out, while a low standard deviation means that the data values are closer together. The actual value of the standard deviation will depend on the context of the data and the units of measurement.

5. How can standard deviation be used in data analysis?

Standard deviation can be used in data analysis to identify outliers, compare the variability between different data sets, and to calculate confidence intervals. It can also be used to assess the normality of a data set and to make predictions based on the spread of the data.

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