# Mayfield High School - Investigating the difference in height of both sexes, comparing years 7 and 11.

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Introduction

## Maths Coursework: Mayfield High School

PLANNING

Aim: To investigate the difference in height of both sexes, comparing years 7 and 11.

- How will the average heights differ between years and sexes?
- Will the girls have a larger range of heights in year 7 than the boys and why?
- Will the boys have a larger range of heights in year 11 and why?
- How will the standard deviation differ between years?

Hypothesis:

I expect that:

- The average height for the boys in year 7 is going to be slightly smaller than that of the girls, though I don’t expect the margin to be a big one.
- I also believe that the boy’s heights in year 11 are going to be larger than the girls in year 11 (though I expect this margin to be larger than the difference in year 7.)
- I expect the standard deviation for the heights of girls in year 7 to be larger than the standard deviation for the boys, which should be smaller.
- For year 11, I believe the standard deviation for the boys will be larger, and the girls one to be smaller in comparison to year 7.

I believe statement (a) because in year 7, at the age of 10-11, more girls will have hit puberty in comparison to boys, and therefore more girls will have had their growth spurt. I expect statement (b) to be true because boys almost always end up taller than girls, and by the age of 15-16 many will have stopped growing and therefore reached their end height. I believe the girls will have the biggest range of heights in year 7 [statement (c)], since there will be a bigger difference between those girls who have grown, and those who haven’t yet started.

Middle

The data for the girls clearly shows the anomalous pieces of data to be significantly different from the rest, along with one more value significantly lower than average in height. Almost all the girl’s heights are grouped around the 1.6 metre mark, and the scatter graph shows a strong grouping. For the boys, their data points are still clearly all in the same region, though are less strongly grouped than the girls. I did expect the heights to be spread over a slightly larger range, though my data has so far suggested that I was wrong.

Another thing that can be found out from the scatter graphs for each sex is the gradient of the line of best fit. The equation for the gradient of a line can be calculated either by using the equation y = mx + c, or by using th following formula:

Change in y (vertical change)

Change in x (horizontal change)

Having the gradient of the line would enable us to predict the height or weight of someone, if we already have one piece of data. An extension of this can be used to determine the probability of a person’s weight (from the sample) lying in a certain range. The equations for each line on the scatter graph are:

Year 7 Boys: y = 93.573x – 97.245

Girls: y = 64.033x – 52.732

Year 11 Boys: y = 33.38x – 2.2796

Girls: y = 13.096x + 29.873

(without 2 anomalies, y = 55.6x – 39.7674)

Cumulative Frequency:

The cumulative frequency is the running total of frequency at the end of each class interval, and is useful when comparing continuous data; it is possible to read off the median, lower and upper quartiles and the interquartile range from the curve, which will be essential for graphs later on in my project.

Conclusion

Summary:

###### Year 7

- Boys have a larger mean by 5cm.

- The girls have a larger median (1.55m for the boys compared to 1.56m for the girls.)

- The girls have the largest range of 0.55, compared to the boys 0.3

- The modal class interval was 1.5-1.6 for both sexes.

- The cumulative frequency curves for both boys and girls are very similar.
- The Box and Whisker diagrams show that the boys interquartile is almost half that for the girls, and that both Q2 lines are skewed to the right showing there to be more taller people.
- The standard deviation was bigger for the girls than for the boys.

- Year 11

- The boys have the larger mean by 9cm (increased the margin by which they’re bigger from year 7)

- The median for the girls is 8cm underneath the median for the boys (1.62m compared to 1.7m)

- The range for the girls range is smaller than they boys by 0.11- the girls having a range of 0.23 and the boys 0.34.

- The modal class interval is 1.6-1.7 for each sex.

- The cumulative frequency curves show the girls heights peaking earlier compared the boys.
- The Box and Whisker diagrams show both the boys and the girls diagrams to be negatively skewed, to the left. They also show the fact that the ranges in year 11 are significantly smaller than in year 11.
- The standard deviation was again bigger for the girls (0.104 compared to 0.143) representing the girl’s larger range.

Appendix:

If I had had more time, I would have also liked to have looked into these following aspects of data sampling:

- Predictions of height and weight using the information from my sampling.
- Probability of a pupil’s height lying within a given range.
- An investigation into body mass index and/or weight as well.
- A further investigation into height, and maybe use exact age as opposed to year group. I could take a larger sample of students, and take more exact calculations etc.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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