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  • Level: GCSE
  • Subject: Maths
  • Word count: 3162

Mayfield High School

Extracts from this document...

Introduction

Jenny Han

Mayfield High School- Statistics Coursework

This coursework is a statistic piece. There are 1183 pieces of secondary data from Mayfield High School. Since there is too much data to do my investigation, I needed to cut down the information to about 60-125 pieces of data.

Two way table

This is used to show different data against each other:

Year Group

Number of Boys

Number of Girls

Total

7

151

131

282

8

145

125

270

9

118

143

261

10

106

94

200

11

84

86

170

Total

604

579

1183

To make it fair there are a few ways of selecting data:

  • Random sample
  • Systematic sample
  • Quota sample
  • Cluster sample
  • Stratified sample

I will be using the Random sampling method. To make it fairer I will have to put 30 girls in one hat and 30 boys in the other. Then again I would have to separate it into 2 year groups so it could link in with my hypothesis. I will need 4 hats, 1 for 15 year 8 girls, another for 15 year 8 boys, 1 for 15 year 10 boys and another for 15 year 10 girls. This will make my data more reliable and unbiased. This has narrowed my data down to 60 which will be enough for my hypothesis 1 and 2. Using different statistical methods would help me through this investigation to help me prove whether my hypothesis correct of incorrect. Graphs such as scatter diagrams, Cumulative frequency, Box plots, Frequency polygons and many more.

Hypothesis

A hypothesis is like a theory which has not yet been proven. In this investigation I am trying to prove that my hypothesis is correct.

The hypothesis I decided to choose were:

  • ‘The higher the IQ the higher your KS2 results ’

...read more.

Middle

5

115

575

Total

30

3040

As you can see the totals end up being the same therefore everything should be the same.

Mean= 3040/30

         = 101.3

Median= 30+1/2

            = 31/2

            = 15.5

Therefore the median would come between…

5+6=11 ← The number 15.5 lies in this so the median is…90 < x ≤ 100

11+14=25 ← This is too big so it isn’t the median.

Median Number lies within:

90 < x ≤ 100

Mode= 100 < x <110

Since it has the most occurring data within its group.

Looking at this table is shows that most year 10 IQ lies between 100 < x ≤ 110. Year 10’s don’t have a 70 < x ≤ 80 because there are no IQs that are under 80. The IQ for year 10s however are more evened out with more numbers on each category. This table shows me that nearly half of the years 10’s have an average IQ.

I am now going to do a frequency table for Ks2 results.

Year 8 Ks2 results:

Ks2 Results

Frequency

Midpoint (x)

fx

2< x ≤ 2.5

1

2.25

2.25

2.5 < x ≤ 3

0

2.75

0

3 < x ≤ 3.5

2

3.25

6.5

3.5 < x ≤ 4

9

3.75

31.5

4 < x ≤ 4.5

8

4.25

34

4.5 < x≤ 5

10

4.75

47.5

Total

30

121.75

Mean= 121.75/30

         = 4.0583

Median= 30+1/2

            = 31/2

            = 15.5

Therefore the median would come between…

1+0=1

1+2=3

3+9=12 ← The number 15.5 lies in this so the median is…3.5 < x ≤ 4

12+8=20 ← This is too big so it isn’t the median.

Median Number lies within:

3.5 < x ≤ 4

Mode= 4.5 < x ≤ 5

Since it has the most occurring data within its group.

The table shows me that most year 8 Ks2 results lie in the average from 3.5 to 5. This tells me that year 8’s are fairly smart and done quite well in their SATs. There are not many year 8’s who got less than 3.5 because the majority got higher. This table tells me that 4.5 < x≤ 5 has the highest frequency.

Year 10 Ks2 Results:

Ks2 Results

Frequency

Midpoint

fx

2.5 < x ≤ 3

5

2.75

13.75

3 < x ≤ 3.5

5

3.25

16.25

3.5 < x ≤ 4

6

3.75

22.5

4 < x ≤ 4.5

6

4.25

17

4.5 < x ≤ 5

8

4.75

33.25

Total

30

102.75

Mean= 102.75/30

          = 3.425

Median= 30+1/2

            = 31/2

            = 15.5

Therefore the median would come between…

5+5=10 ← The number 15.5 lies in this so the median is…3 < x ≤ 3.5

10+6=16 ← This is too big so it isn’t the median.

Median Number lies within:

3 < x ≤ 3.5

Mode= 4.5 < x ≤ 5

Since it has the most occurring data within its group.

Looking at this table, the frequency is spread out. This means that the student’s intelligence spread evenly. Some are clever and some not so clever. The frequency gets higher slowly which means there are smarter people. This table tells me that 4.5 < x ≤ 5 got the highest frequency.

Comparison between Year 8 and 10 IQ:

Looking at both tables it shows that year 8 IQs lie around 90 < x ≤ 100 and 100 < x ≤ 110 whereas in year 10 most lie in 100 < x ≤ 110. Since most year 10’s are in 100 < x ≤ 110 this means that they are smarter because nearly half are in this group. Year 8’s however have less people in 80 < x ≤ 90 than the year 10 but no year 10’s got lower than 80 which meant that year 10’s had a higher IQ overall.

Comparison between Year 8 and year 10 Ks2 Results:

Year 8’s have a wider range of Ks2 results. They vary from the mean of 2 to 5 whereas year 10 has less, from 2.5 to 5. Since year 10 have less it means they should have better results but year 8’s have a higher frequency in the 4.5 < x ≤ 5 group which is the highest.

Looking at both results it shows me that the Year 10’s have a higher IQ and ks2 results. The range for year 10’s is much smaller than year 8’s on the ks2 results. Therefore linking with my hypothesis, it tells me that it is right.

I haven’t got enough to show that my hypothesis is correct just yet so I will now move on to cumulative frequency. This will help me further in my investigation.

Cumulative Frequency Tables:

Cumulative frequency is when you add up the frequency as you go along.

Eg.

IQ

70-80

81-90

91-100

Frequency

1

1

11

C.Frequency

1

2

13

...read more.

Conclusion

The algebraic equation is:

image02.png

The ‘n-1’ could be replaced by just n

X bar is the mean of x

N is the number of items

F=frequency

I will now use standard deviation to help me show that my hypothesis is correct.

Year 8:

IQ

Frequency

Midpoint (x)

fx

x-xbar

(x-xbar)2

f(x-xbar)2

70 < x ≤ 80

1

75

75

-20

0

80 < x ≤ 90

1

85

85

-10

90 < x ≤ 100

11

95

1045

0

100 < x ≤ 110

12

105

1260

10

110 < x ≤ 120

5

115

575

20

Total

30

Mean=95

3040

Year 10:

IQ

Frequency

Midpoint (x)

fx

x-xbar

(x-xbar)2

f(x-xbar)2

80 < x ≤ 90

5

85

425

7.5

56.25

90 < x ≤ 100

6

95

570

17.5

306.25

100 < x ≤ 110

14

105

1470

27.5

756.25

110 < x ≤ 120

5

115

575

37.5

1406.5

Total

30

Mean:77.5

3040

Conclusion of Hypothesis 2:

Overall, I think that I have done enough to show that my hypothesis was correct. I am saying this because all my graphs support my hypothesis that Year 10’s have a higher IQ and better Ks2 results. I believe that my sample wasn’t large enough because there wasn’t enough data to plot my graphs and it was quite hard dealing with the shortage. Also if there was more data it would have been more accurate. If I were going to do the investigation again, the things I would do differently was to pick more data.

What I found out:

  • There was a positive correlation, so that means that the higher the IQ, the better the

Ks2 results.

  • The grouped data showed me that there was more year 10’s with a higher IQ than year 8’s and the same with Ks2 results.
  • Cumulative frequency showed that Year 10 have a higher IQ and Ks2 median.
  • The histogram and frequency polygon showed that also more year 10’s had a higher IQ and ks2 results.

Mayfield High School- Statistics Coursework

...read more.

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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