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• Level: GCSE
• Subject: Maths
• Word count: 1016

# Investigating the hypotheses - &quot;Secondary school students grow taller as they grow older&quot; and &quot;Female secondary school students grow taller earlier before their male counterparts&quot;

Extracts from this document...

Introduction

Title:

Contents:

Introduction:

Hypothesis 1 "Secondary school students grow taller as they grow older"

Hypothesis 2: "Female secondary school students grow taller earlier before their male counterparts"

Course of action (COA):

(This is how I’m going to prove the above)

To investigate the stated hypothesis, data regarding heights of students in various year groups was collected. This data was then separated into year groups and further into gender. This data was then randomly sampled and 40 items of data were selected from each year group, 20 from the male group and 20 from the female group.

total randomly sampled data items = 5 * 40 =200.

NOTE:

You have to show that you understand that these values are ‘estimates’. For example the mean average of height for males in year 7 which we calculate after grouping the data will not be the same as the value if you add all the heights together and divide by how many you have. This is because of grouping the data. The thing is, we have to do this because of the shear volume of data we have. It is not feasible to do the former ( add them all together).

Middle

Mode: The value that occurs to most, which frequency is the highest, that is your modal interval, the midpoint is taken as the mode. So for year 7, all, highest frequency is 16, interval 150-159.  The mode is taken as 154.5. This shows that the averages are similar, so they are concurrent, so they backup my calculations.

Range:  shows you the range of data. Highest value – Lowest value.

Inter Quartile Range = UpperQuartile – LowerQ

Lower Quartile = ¼ of the way along value. 25th percentile. Y7, all =

Upper Quartile = ¾ of the way along value. Or the 75th percentile.

* using c.f.  graphs UQ & LQ determined and the IQR calculated to determine box and whisker plots drawn as well seperate sheet

• standard deviation also calculated upon each set.  (put on same sheet as mean median)

standered deviation : is the amount by which the heights deviate which means spread out from the mean. So the higher the sd, the more the heights are spread from the mean.

• % change of median height in each year group -- new sheet and with that draw pie charts of these.

Conclusion

/td>

Mean

Sigma fx / n

IQR = Upper Quartile - Lower Quartile.

154.5-144.5=10

6000 / 40

UQ = the value 3/4 of the way along the group.

10th position

140-149 = 144.5

150

LQ= the value 1/4 of the way along the group.

30th position

150-159=154.5

Median = 1/2 way along.

Median:

(n + 1) / 2

41 / 2

20.5 value

sd = sqr_root(((sigma fx^2)/f) - mean^2)

9.20597632

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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