Standard Deviation of Mean Question (Further Maths GCSE)

[Cramlington567]

Hi, my son is struggling with question A on the pictured sheet. Can anyone give us a clue how we go about this? He wants to understand this for next week's exam.

It is mainly A but any insight on question B at the bottom of the page also welcome. Thanks

The picture you have posted appears blurred to me. If you PM me a clear picture, I might be able to help.

Trying again.

Does he know how to calculate the standard deviation of a set of numbers?

If not then he needs to revise it from scratch
https://www.bbc.co.uk/bitesize/guides/zcjv4wx/revision/2

We need to see the top 1/3 of the page not just the histogram to advise

You can't calculate the actual standard deviation from grouped data you need to get an estimate (because you don't have the actual data).

There is an example of how to do it here.

www.statology.org/mean-standard-deviation-grouped-data/

Basically you estimate the mean.

You then work out for each data point, assuming each data point is at the middle of the group, the distance between it and the mean, you then square the distance.

Add up all the distances and then take the positive square root.

Question b this data is not normally distributed because the normal distribution is symmetric and this data is not symmetric

OR

For the normal distribution 68% of data is within 1 standard deviation of the mean so if the answer to a is not 68% the distribution is not normal.

Oh of course, yes, because the picture was fuzzy I missed that it was grouped.

Hope this will help.

Hope this will help.

Very helpful answers. Thanks so much. He gets it now. Great to see his face as it clicked.

Good!

Tell him to show all his workings clearly.

And to only round the final answer.