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a level maths statistics LINEAR INTERPOLATION

stuck a bit on this question, specifically part (b)
i get an answer about 2 units out of the real result
Reply 1
Avatar for hj!gz
hj!gz
OP
12
Capture.PNG
Reply 2
Avatar for mqb2766
mqb2766
21
Original post by hj!gz
Capture.PNG

Can you upload your attempt?
Reply 3
Avatar for hj!gz
hj!gz
OP
12
yeah, of course

a. mean = £10.22
standard deviation = £1.35

b. mean + standard deviation = 11.57

11.57 - 11 = x - 50
12 - 11 65 - 50


(x represents the cumulative frequency amount of less than 11.57)

x = 58.55

so answer = 80 - 58.55
= 21.45
Reply 4
Avatar for mqb2766
mqb2766
21
Original post by hj!gz
yeah, of course

a. mean = £10.22
standard deviation = £1.35

b. mean + standard deviation = 11.57

11.57 - 11 = x - 50
12 - 11 65 - 50


(x represents the cumulative frequency amount of less than 11.57)

x = 58.55

so answer = 80 - 58.55
= 21.45

Sorry for the late reply, I missed the notification.
Agree for mean and std dev up to the 11.57.

Note that if it was 11.5, the answer would be 20. The linear interpolation should go from 11.5 to 12.5, and for a quick guestimate with 11.57 subtract 1 or 2 from 20.
(edited 4 years ago)
To expand a little on what mqb2766 has said.

The data is rounded to the nearest pound, so the class boundaries are 7.5, 8.5, 9.5, 10.5, 11.5, 12.5
Reply 6
Avatar for hj!gz
hj!gz
OP
12
okay, thank you very much, both of you!

close but not close enough for me.
Reply 7
Avatar for mqb2766
mqb2766
21
Original post by hj!gz
okay, thank you very much, both of you!

close but not close enough for me.


The key thing is to pay attention to how the intervals are defined. Other than that you were fine.

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