Mean and Standard deviation

Can someone help me? I know how to do these types of questions but I don't understand the format of it:

20 pieces of data have been summarised as follows: Σ(x+2)=7 and Σ(x+22)^2=80.

Calculate the mean and standard deviation of the data.

You should know the formulae for mean and std dev (or var) so its really just about rearraning the given information. The mean is
mean = Σx / n
so by rearranging the Σ(x+2)=7 you can get what Σx is and therefore the mean. The std dev is similar but you usually work with the variance which is just (std dev)^2..

Post what youve tried to do.

I have no idea on how to start. I have the answers (mean = -33/20 and s.d= 1.97 to 3sf) but how do you get there?

There should be an example in your textbook, but if youre adding 2 to each of the elements, how much do you add to the sum? So the sum = ... and therefore the mean = ..

Would you mind just working it out for me so that I can see and understand what youre doing? I'm not really understanding, I think it might be because it's late lol

I know that n=20 and thats about it

Yes, I can help you!
...

It should be under linear coding in your textbook, though for the mean calculation you could view it relatively simply. You know the sum of the 20 examples when you add 2 to each of the 20 data points (7), so just work it throgh.
https://sites.google.com/view/tlmaths/home/a-level-maths/as-only/l-data-presentation-interpretation/l3-central-tendency-variation
has some examples

Yes, I can help you!
To find the mean, you need to use the formula:
Mean = (sum of all the data) / (number of data)
Here, we have the sum of (x+2), which is Σ(x+2) = 7. We can use this information to find the sum of all the data:
Sum of all the data = Σ(x+2) - Σ2 = 7 - 2*20 = -33
To find the number of data, we can notice that each data point is represented as (x+2). So, if we subtract 2 from each data point, we will get the original data. Since we have 20 data points, the number of data is also 20.
Therefore, the mean is:
Mean = (sum of all the data) / (number of data)
= (-33) / 20
= -1.65
To find the standard deviation, you need to use the formula:
Standard deviation = sqrt((sum of squares of deviations) / (number of data - 1))
Here, we have the sum of (x+22)^2, which is Σ(x+22)^2 = 80. We can use this information to find the sum of squares of deviations:
Sum of squares of deviations = Σ(x+22)^2 - Σ2 = 80 - 2*20*22 + 20*22^2 = 5860
Therefore, the standard deviation is:
Standard deviation = sqrt((sum of squares of deviations) / (number of data - 1))
= sqrt(5860 / 19)
≈ 9.10 (rounded to two decimal places)
So, the mean of the data is -1.65 and the standard deviation is approximately 9.10.

it would be worth reading the forum guidelines (sticky at the top of the forum) about giving hints etc, rather than solutions

Yes, I can help you!
To find the mean, you need to use the formula:
Mean = (sum of all the data) / (number of data)
Here, we have the sum of (x+2), which is Σ(x+2) = 7. We can use this information to find the sum of all the data:
Sum of all the data = Σ(x+2) - Σ2 = 7 - 2*20 = -33
To find the number of data, we can notice that each data point is represented as (x+2). So, if we subtract 2 from each data point, we will get the original data. Since we have 20 data points, the number of data is also 20.
Therefore, the mean is:
Mean = (sum of all the data) / (number of data)
= (-33) / 20
= -1.65
To find the standard deviation, you need to use the formula:
Standard deviation = sqrt((sum of squares of deviations) / (number of data - 1))
Here, we have the sum of (x+22)^2, which is Σ(x+22)^2 = 80. We can use this information to find the sum of squares of deviations:
Sum of squares of deviations = Σ(x+22)^2 - Σ2 = 80 - 2*20*22 + 20*22^2 = 5860
Therefore, the standard deviation is:
Standard deviation = sqrt((sum of squares of deviations) / (number of data - 1))
= sqrt(5860 / 19)
≈ 9.10 (rounded to two decimal places)
So, the mean of the data is -1.65 and the standard deviation is approximately 9.10.