I have to calculate first how many random pupils to examine in general.

10% of 713 (0.10 × 713) equals 71.3, which to the nearest integer is 71. This outcome is too high.

5% of 713 (0.05 × 713) equals 35.65, which to the nearest integer is 36. This outcome is loo low.

There we find the median between 10 and 5, which approximately are 7.

Therefore, 7% of 713 (0.07 × 713) equals 49.91, which to the nearest integer is 50. This is a reliable result.

Second, I have to calculate how many pupils to examine within each year because each year group varies in total amount of students.

This is where I have to use stratified sampling.

We calculate the proportion of pupils from each of the year groups.

= 282 ÷ 713 × 50 = 20 pupils

= 261 ÷ 713 × 50 = 18 pupils

= 170 ÷ 713 × 50 = 12 pupils

Total = 50

So,

From year 7 I will pick 20 students

9 I will pick 18 students

11 I will pick 12 students

And finally I have to decide how to systematically select the number of pupils for each year.

NB: Number of students varies in different. This must be done carefully.

I will do this by dividing the total number off students by the different strata outcome.

Year 7 = I will pick ever 14th student going down the list, I have come to this decision by 282/20 = 14.1 = 14

Year 9 = I will pick ever 14th student

261/18 = 14.4 = 14

Year 11 = I will pick ever 14th student

170/12 = 14.1 = 14

Now that have obtain sampling data I can begin comparing IQ with KS results and I can I begin to give evidence to prove my hypothesis.

3. Evidence

To obtain evidence I will be used a series of methods:

- Scatter Diagrams, Correlation and lines of best fit
- Group and Continuous data
- Measures of average in grouped and continuous data
- Cumulative frequency, interquartile range and box plot
- Histograms and frequency density

Tables of attributes of IQ and Key Stage result for years 7, 9 and 11 on next page.

Year 7 Table

Student Number Ascending

## IQ Ascending

## Year 9 Table

Student Number Ascending

###
IQ Ascending

## Year 11 Table

## Student Number Ascending

### IQ Ascending

Year 7 - Scatter Graph, Correlation and lines of best fit

This graph shows a moderate correlation and has a positive correlation. This scatter graph shows a strong link to my hypothesis. From the correlation of the graph we can see that the scatter graph backs up my hypothesis, “Higher IQ means, enhanced skill in understand of the subject, leading to better results in exams.”

Because as we can see, as the IQ on the graph increases so does the KS results.

All the figures but one relate to my hypothesis.

This result is circled to indicate that it clash from all the other result and argues the hypothesis.

This result may’ve occurred for any reason.

E.g. the data was collected incorrectly, maybe a printing error etc.

Year 7 - Group and Continuous data and measures of average in grouped and continuous data

This is group data

Total 20 IIII IIII IIII IIII 78

These are the measurements:

Mean = (15+63)

20

Modal Group = 4–5

Median = 20

2

The mean shows the average KS results are 3.9 however 70% of students got a level 4-5.

The is continuous data

Mean = (30.5+0+70.5+724+1105)

20

Modal group = 101-120

Median = 20

2

As we can see the average IQ in year 7 are 96.5, however 50% of the year has an IQ of 101 – 120.

Year 7 - Cumulative frequency

So from the cumulative frequency curve for this data, we get these results:

Median: 101

Lower quartile: 95

Upper quartile: 108

Inter-quartile range: 13 (108-95)

Year 7 - Histograms and frequency density

Frequency frequency

density class width

Class boundaries = 1, 91, 96, 101, 106, 111, 116

Class width = 90, 5, 5, 5, 5, 5

Year 9 - Scatter Graph, Correlation and lines of best fit

This graph shows a slightly moderate correlation and has a positive correlation. This scatter graph shows again a strong link to my hypothesis. As we can see as the IQ raises the KS results increases therefore the graph is good evidence to support my hypothesis.

Again all the figures but one relates to my hypothesis.

This result is circled to indicate and has no correlation to the line of best fit.

This result may’ve occurred for any reason.

E.g. the data was collected incorrectly, maybe a printing error etc.

Year 9 - Group and Continuous data and measures of average in grouped and continuous data

This is group data

These are the measurements:

Mean = (5+72)

18

Modal Group = 4–5

Median = 18

2

The mean shows the average KS results are 4.27 therefore 88% of students got a level 4-5.

The is continuous data

Mean = (10.5+0+0+70.5+633.5+994.5)

18

Modal group = 101-120

Median = 18

2

As we can see the average IQ in year 9 are 94.44, however 50% of the year has an IQ of 101 – 120.

Year 9 - Cumulative frequency

So from the cumulative frequency curve for this data, we get these results:

Median: 100

Lower quartile: 97

Upper quartile: 110

Inter-quartile range: 13 (110-97)

Year 9 - Histograms and frequency density

Frequency frequency

density class width

Class boundaries = 1, 91, 101, 106, 111, 116, 121

Class width = 90, 10, 5, 5, 5, 5,

Year 11 - Scatter Graph, Correlation and lines of best fit

This graph shows a strong correlation and has a positive correlation. This scatter graph shows again a strong link to my hypothesis and has the best correlation in order to give evidence for my hypothesis. As we can see as the IQ raises in proportion to the KS results.

The graph has two imprecise results however these results are not too inaccurate and they still can be used to support my hypothesis.

This result is circled to indicate and has no correlation to the line of best fit.

Year 11 - Group and Continuous data and measures of average in grouped and continuous data

This is group data

These are the measurements:

Mean = (12.5+31.5)

12

Modal Group = 4–5

Median = 12

2

The mean shows the average KS results are 3.6 however 58% of students got a level 4-5.

The is continuous data

Mean = (171+382+422+231)

12

Modal group = 91 - 100

Median = 12

2

As we can see the average IQ in year 11 are 100.5, therefore 33% of the year has an IQ of 91 – 100.

Year 11 - Cumulative frequency

So from the cumulative frequency curve for this data, we get these results:

Median: 100

Lower quartile: 93

Upper quartile: 105

Inter-quartile range: 12 (105-93)

Year 11 - Histograms and frequency density

Frequency frequency

density class width

Class boundaries = 86, 91, 101, 106, 111, 121

Class width = 5, 10, 5, 5, 10,

4. Evaluation

I predicted that the higher a pupils IQ the higher their results in key stage results in examinations.

From my graphs and table we can see that this theory was correct. In my scatter graph there was a strong relationship between IQ and key stage results, however I can not be sure that the relationship is genuine, because the data collected is only from one school, I may get different results if I was to research more school and collect more data.

All my results were done in the most reliable way with as much detail possible.

With these results, schools can easily predict a student’s result in an exam by there IQ. This can be useful when teachers want to organise which tier a student should take or when colleges would want to accept students with good results.

Predicting results is very easy. If you refer back to one of the scatter graphs you can produces improvements on it.

This is done by drawing a horizontal line from IQ to the line of best and then a vertical line down to results we can predict a results for a particular IQ.