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HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Standard Mathematics => Topic started by: dani01 on October 22, 2019, 12:30:42 pm

Title: Median from cumulative frequency table
Post by: dani01 on October 22, 2019, 12:30:42 pm

Hi would someone be able to explain to me why the answer is b?
I worked it out by doing half of 32 which is 16. the 16th score is 19. so why is the answer 19.5??
thanks

Title: Re: Median from cumulative frequency table
Post by: RuiAce on October 22, 2019, 12:42:15 pm

Quote from: dani01 on October 22, 2019, 12:30:42 pm

Hi would someone be able to explain to me why the answer is b?
I worked it out by doing half of 32 which is 16. the 16th score is 19. so why is the answer 19.5??
thanks

If you list out the scores, you get:
17 17 17 18 18 18 18 18 18 19 19 19 19 19 19 19 20 20 21 21 22 22 22 22 22 22 22 22 22 23 23 23

Now try to find the median using the cross-out-numbers-from-both-sides method. You'll find that you end up with both the 19 and the 20 left. So using that old method, you would get 19.5.

So where's the conflict? In reality, half of 32 is not correct. The formula for the median is the \( \frac{n+1}{2} \)-th score, not the \( \frac{n}{2}\)-th score. So you actually have to compute \( \frac{33}{2} \), which is equal to \(16.5\). Hence, you need to compare both the 16th score, and the 17th score.