Linear interpolation help!!!

I don't get how to do linear interpolation to work out part d it's just not working

I don't get how to do linear interpolation to work out part d it's just not working

Is this question from one of the Edexcel textbooks?

What did you get for the mean and std dev and how did you try to do the linear interpolation?

Er okay; calculate the maximum gust of wind within 1 std deviation and figure out which category it is in; once you have done that add another column to the table with cumulative frequency: plot a cumulative frequency graph and look for the segment line which represents your category: calculate the gradient of this line using the upper and lower bounds with the upper and lower frequencies; and then form an equation with your maximum gust of wind .within one standard deviation and x to denote its frequency: this will again be a gradient equation with 2 known x,y values and since you worked out the gradient of the line earlier you can solve the equation

For the mean I got 23.4 and std dev: 7.32
I then added the mean and standard deviation and got 30.72 and then used linear interpolation but got 22.43?

I know it would be easier to show my working out but I can't at the moment

https://www.physicsandmathstutor.com/maths-revision/solutionbanks/edexcel-statistics-mechanics-year-1/

Worked answer will be on there

Ummmm this seems so longgg is there no other way without working out the gradient etc?

Yeah I had a look at that but I don't get it still

Obviously you want the mean +/- std dev so approximately 16 <-> 31. 16 lies in the 2nd interval and 31 in the last interval.
Just do the linear interpolation on each of these intervals. Not much working ...

Hang on, so the 16 and 31 represent the intervals and not the frequency? I thought they were the frequencies that's how I ended up with the wrong intervals. Right, okay makes sense thanks

should only take about 3 mins; you only need to do the gradient of the specific category's line and you needn't plot the graph; there are other methods tho

Oh okayyyy I prefer another method but thank you anywayy

Obviously you want the mean +/- std dev so approximately 16 <-> 31. 16 lies in the 2nd interval and 31 in the last interval.
Just do the linear interpolation on each of these intervals. Not much working ...

Okay I worked it out I got 50.252 and then 6.3
But they subtracted them? Why is that?

They want the number of days its within the range, so the "width" of the frequencies.

I don't get how to do linear interpolation to work out part d it's just not working