Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 321

Frequency Tables; midpoints

What is the midpoint of the following class interval;

140 < h ≤ 150 ?

I’m used to seeing it given as 145 in this kind of example. But is it?

The possible values for h are, I think;

141,142,143,144,145,146,147,148,149,150.

The middle value of that group is, I think,145.5

So why is the midpoint of that class interval usually given as 145?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Frequency Tables; midpoints

You would need to know what 'h' represents.  140 <  h  ≤ 150 implies h can have any value above 140 with an inclusive upper bound of 150. So h could be 140.000000000001

If you draw a number line with those endpoints, 145 is half way along (and having one excluded endpoint and one included does not alter that).

If only the numbers {141,142,143,144,145,146,147,148,149,150} are under consideration such as "What is the median of these ten numbers: 141,142,143,144,145,146,147,148,149,150" then 145.5 is correct.

So median and middle number may not be the same thing.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Frequency Tables; midpoints

Thanks, Bob

h was for height (of tomato plants)

So, 140.000000001 etc makes sense.

My first thought was, "Greater than 140 therefore 141, 142..."

Doh!

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Prioritise. Persevere. No pain, no gain.