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• Level: GCSE
• Subject: Maths
• Word count: 1488

# Mayfield High. From my scientific knowledge I know that at KS3 girls grow faster than boys. I will check this by drawing a frequency table.

Extracts from this document...

Introduction

Pilot Test

The preliminary test above gives us a rough idea about the pupils. To do this I used systematic sampling. This is done by starting with a random sample and selecting every nth number after another. In my case I used every second number of my sample. I will use this pilot test  to determine the reliability of the data as the data is a secondary source. It has a slight positive correlation. This shows me that the data is more likely to be reliable.

Hypothesis 1

From my scientific knowledge I know that at KS3 girls grow faster than boys. I  will check this by drawing a frequency table. I will then draw a histogram for boys and girls, then a cumulative frequency graph with a box plot which contains the data for both boys and girls. Using this information I can then analyse and confirm if my hypothesis is wrong or right.

I will use a grouped a frequency table because it makes the data organised. However the disadvantage of using a frequency table is that we lose accuracy as we have grouped the data.

Key Stage 3 Girl’s Height

Middle

Variance = 0.01991

The mean of the girls’ height is 1.56. The mean of the boys’ 1.58. These are only estimates because they are rounded and the values are different. I rounded these answers to 2 decimal places.  The mean shows me that KS3 boys are taller than KS3 girls.

The histogram above is for KS3 girls. The highest height of the bar for girls is between 1.60m and 1.65m. This tells me that most KS3 girls height is between 1.60m and 1.65m. There are 9 girls that are that are that height.. The lowest height of bars are between 1.70m and 1.80m. There is 1 girl for both of those heights.

The histogram above are for KS3 boys. The highest height of the bar is between 1.50m and 1.55m. There are 7 boys which are this height. There re a few bars which have values which are 0. This shows that the heights are varied.

Cumulative Frequency For KS3

The cumulative frequency graph and box plot I can compare the results and fully verify my hypothesis.

Using the graph I obtained these statistics for KS3 Girls:

Mode:                                  1.60-1.65m

Range:                          0.4m

Lower Quartile:                   1.48m

Median:                          1.58m

Upper Quartile:                   1.63m

Interquartile Range:                  1.63-1.48=0.15m

Q1 -1.5xIQR:                1.705

Q3+1.5xIQR:                1.855

Conclusion

organised. However the disadvantage of using a frequency table is that we lose accuracy as we have grouped the data.

Key Stage 4 Girls’ Height

Table of Values of Histogram [Key Stage 4 Girl's Height]:

Class Int.        Mid. Int. (x)        Class Width        Freq.        Cum. Freq.

1.4 = x < 1.45        1.425        0.05        1        1

1.45 = x < 1.5        1.475        0.05        0        1

1.5 = x < 1.55        1.525        0.05        1        2

1.55 = x < 1.6        1.575        0.05        4        6

1.6 = x < 1.65        1.625        0.05        3        9

1.65 = x < 1.7        1.675        0.05        2        11

1.7 = x < 1.75        1.725        0.05        1        12

1.75 = x < 1.8        1.775        0.05        1        13

f = 13

fx = 20.97

fx² = 33.94

Mean = 1.613

Standard Deviation = 0.08583

Variance = 0.007367

Key Stage 4 Boys’ Height

Table of Values of Histogram [Key Stage 4 Boy's Height]:

Class Int.        Mid. Int. (x)        Class Width        Freq.        Cum. Freq.

1.5 = x < 1.55        1.525        0.05        1        1

1.55 = x < 1.6        1.575        0.05        0        1

1.6 = x < 1.65        1.625        0.05        1        2

1.65 = x < 1.7        1.675        0.05        2        4

1.7 = x < 1.75        1.725        0.05        1        5

1.75 = x < 1.8        1.775        0.05        5        10

1.8 = x < 1.85        1.825        0.05        2        12

1.85 = x < 1.9        1.875        0.05        1        13

1.9 = x < 1.95        1.925        0.05        1        14

f = 14

fx = 24.55

fx² = 43.19

Mean = 1.754

Standard Deviation = 0.09949

Variance = 0.009898

Key Stage 4 Boy’s Height

Height & Weight of  all Boys

Height & Weight of all Girls

The scatter diagram above is for all girls in Mayfield high. It shows a strong positive correlation between the height and weight of all girls. The equation of the line of best fit is y= 20.54+ 37.5. The centroid of all my points lies on the co-ordinates (1.584,49.32).  The positive correlation shows that the taller you are the heavier you are. The above strong correlation confirms my third hypothesis saying the taller you are the heavier you are.

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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