Challanging maths Frequency table?

Question

What is a and b, i need working to be shown.
This table shows the weights of 100 children in year 7,
An estimate of the mean weight of the children is calculated as 44 kg.

Weight,w(kg) - Frequency
20 < w 30< w 40 50 60

Answer 1

It's similar to two equations, two unknowns:
Total number of children = 100, so...
12+21+38+a+b=100
Mean weight = 44, so...
You must offset the amount of children in the first two categories (and you only have 29 kids to work with).
Therefore, since there are 33 kids in the first two weight classes you need more in the heavier of the last two than the ratio was for the light to heavy for the first two.
Also, the mean is slightly to the low end of the middle class, so don't put too many in the upper class.
I don't actually know how to get the answer other than guess (I don't even know how to check). I would go with a=14, b=15. Something like that anyway.

Answer 2

12 + 21 + 38 = 71, so 100 - 71 -->

29 = a + b (equation 1)

12(25) + 21 (35) + 38(45) + a(55) + b(65) = 2745 + 55a + 65b = 4400 (avg weight * number of kids)

1655 = 55a + 65b (equation 2)

Equations 1 and 2 can give you the answers via substitution.

1655 = 55(29 - b) + 65 b = 1595 + 10b -->

b = 6 --> a = 23

Answer 3

First, put them in order. Then, what do the numbers represent? Let's say they are scores on a test. Make a column for it. Next put a tally column. I don't really know if you need this one, but this is what I was taught. Last, put a frequency column. The frequency is the number of times a number appears in the data. It should look something like this: | Score | Tally | Frequency | 94______|............... 1 95______|............... 1 96______|............... 1 105_____|............... 1 110_____|............... 1 114_____|............... 1 116_____|............... 1 123_____|............... 1 126_____|............... 1 128_____|............... 1 132_____|................1 _____________________________ Sorry about the lines and periods. You can also do it like the guy above me...