Statistics question

P 111 q 8.

(a) This table is a frequency distribution and the second row in tables like this is always the frequency.
You can either be asked to find the mean in which case you multiply each number in the top row by its frequency and add these together and then divide by the sum of the frequencies.
In this case you are given the mean, so, kind of like the simpsons rule example we did today, you set up an equation and solve it.
Left hand side of equation:
You will have 0(1) + 1(x) + etc on top and 1 + x + 1 etc on the bottom.
Right hand side of equation:
This will be the mean which you have been given.
Then you will have an equation with a fraction in it, so you multiply across by whatever is under the line and solve.

(b) See page 103.
The standard deviation is a measure of how spread out data is.
You could have 2 sets of numbers with the same mean eg
1 2 3 4 5 6 7 8 9 10
and
5 5 5 5 5 6 6 6 6 6
both have mean = 5.5, but the standard deviation of the first set would be bigger because the numbers are more spread out.
To find standard deviation you need to first find the mean value and then make a little table:
First column is all the numbers in your list.
Second column is the difference between the number in the 1st column and the mean.
Third column is the number in the 2nd column squared.
Add the values of the third column.
Then divide this number by the number of values.
Then get the square root of the result.
When you have done this take a look at how to find the standard deviation of a frequency distribution.

(c) This is explained on page 96.
When you are making the cumulative frequency table, note that the last number should be 240 (as you are told there are 240 villagers).
When drawing the ogive, make sure that you put the frequency (which is no. of villagers) on the vertical axis. On the horizontal axis you put the values you have in the top row, without the ≤ or < signs.
You graph cumulative frequencies on an ogive.
(i) For the median, you need to find the "middle" villager. Start on the vertical axis.
(ii) The interquartile range is found by finding the difference between the ages of the lower quartile villager and the upper quartile villager.
For both these questions you start on the vertical axis, draw a horizontal line until it reaches the curve, then drop a vertical line to read the age from the horizontal axis.
(iii) For this question, you need to start on the age axis at 55. Then go up to the curve and then across to the vertical axis. Then re-read what the question is asking you.