I intend to investigate the relationship between height and weight

I will make sure that my sample is fair by reducing all the odds of it being biased by using this method which is called 'stratified sampling'. This is because data may be inequitable, for example, there may be more pupils given in one year group than the other. The sample should be kept proportional all throughout my investigation, so that my results can be as unbiased as possible. I will then use the data that I have acquired after using the stratified sampling to select the number of pupils randomly and hopefully prove or disprove the hypotheses that I have made.

Stratified sampling is a sampling method in which the population is divided in to groups (in this case, year groups) and then random samples are taken from each stratum (or layer). There are two ways in which you could do stratified sampling. The first method involves dividing the class size by the total population and then multiplying the result by the size of the sample. The second method is dividing the class size by a hundred and then multiplying the result by the percentage size of the sample.

The calculations that I will have to do are to find the measures of central tendencies, which are the estimated mean, median, mode and range. In a frequency table, the mean would simply be multiplying the 'mid-interval value' by the 'frequency' for each column. Then find the total of the 'mid-interval value times frequency' column and divide that by the 'frequency column' total to then get the estimated mean.

The median is the number in the middle of the whole sequence, presuming that the sequence is set out in ascending order. The mode is the number which appears the most in the sequence. The range is merely the difference between the highest number and the lowest number.

Also two other calculations that I will carry out are standard deviation and Spearman's rank correlation. Standard deviation is the square root of the measure of spread that uses all the data.

Spearman's rank correlation coefficient is a measure of the agreement between two that has been data set. However it can also be described as the method of showing whether any one set of numbers has an effect on another set of numbers.

The way that I will present the information that I have gathered, is by using different charts, graphs and diagrams. The main ones that I will use are tally charts, frequency charts, cumulative frequency/frequency polygon charts, using upper quartile (3/4 of the way up), lower quartile (1/4 of the way up) median and the interquartile (upper quartile minus the lower quartile). Also I may use a box and whisker diagram, and a scatter graph with the line of best fit (with the equation of the line of best fit).

Tally charts are straightforward to use, it helps with counting and displays the frequency of the groups very clearly. The cumulative frequency graph will make it easier to find the upper quartile, lower quartile, interquartile range, median values of data. The box and whisker diagram will be the best possible way to present that data.

The scatter graph is the best way to show how two pieces of data correspond with each other. It can show if there is a strong positive correlation, a strong negative, a weak positive, a weak negative correlation or if there is no correlation at all. We can gain even more information if we include in a line of best fit, with its equation Y=mx+c. The 'Y' in the equation represents the point in the graph, the 'm' represents the gradient, the 'x' represents another point on the graph and finally the 'c' represents the intercept. We use scatter diagrams mostly to compare two variables.

As a result of the calculations and diagrams I intend to produce, I will be able to compare and analyse the recorded data to prove or disprove my hypotheses.

Maths Coursework Rujina Miah 10S