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  • Level: GCSE
  • Subject: Maths
  • Word count: 5551

What affects a persons ability to estimate?

Extracts from this document...

Introduction

By Scott Rentell        Page         28/04/07

GCSE STATISTICS: COURSEWORK

‘WHAT AFFECTS A PERSON’S ABILITY TO ESTIMATE?’

Presentation of data, Calculations and Interpretation and Conclusions:

Now that I have collected all the data, I can now begin to analyse the results and find out whether either: age, intelligence or gender affect a person’s ability to estimate. To begin with I will investigate Age. By beginning with Age I can expand the investigation further by changing the variables one at a time. I will start simply by looking at the year groups and age groups. This will enable me to see whether theirs a difference. I will later go into more depth by comparing years. I will have clear views of the results by using a variety of graphs and charts regularly.

image00.png

I have used the Average and Standard Deviation functions on Microsoft Excel to calculate these results. The answers have been rounded to the nearest 2 decimal places to make it clearer for readers to understand.

A bar graph is below to see the results more clearly and visually:

image01.png

To get an even better view of the spread of results I’ve now put them in a box and whisker diagram, shown below. The calculations for the quartiles I found by using the function ’Quartile’ on Microsoft Excel. By doing this I’ll have a better idea of the dispersion of data these Year groups have.

Observations and conclusions:

- By studying the box and whisker diagrams I can see that both Year 7 and 8 have a large range of estimates between their third and fourth quartiles.

- From looking at the bar chart I can that the Year 11 mean average estimate is closest to the actual line (8.4cm). This makes it look as if Year 11 group are the best at estimating.

...read more.

Middle

Year 7 Lower Set

9.62cm

2.56

Year 8 Higher Set

9.58cm

2.23

Year 8 Lower Set

8.05cm

2.94

Year 9 Higher Set

8.94cm

1.52

Year 9 Lower Set

9.14cm

3.20

Year 10 Higher Set

8.38cm

1.61

Year 10 Lower Set

9.76cm

2.18

Year 11 Higher Set

8.10cm

1.54

Year 11 Lower Set

8.13cm

1.63

image04.png

This line graphs purpose is to compare the Higher Sets to the Lower sets. From simply looking at the graph I can tell that the higher mean averages are to the right of the graph which is where the results of the lower sets are plotted. Towards the left, I can see how the line keeps decreasing as the year groups reach year 11.

Calculations

image05.png

mean average

stan.dev

Year 7 higher set

8.94cm

3.24cm

Year 8 higher set

9.58cm

2.23cm

Year 9 higher set

8.94cm

1.52cm

Year 10 higher set

8.38cm

1.61cm

Year 11 higher set

8.10cm

1.54cm

year 7 lower set

9.62cm

2.56cm

year 8 lower set

8.05cm

2.94cm

year 9 lower set

9.14cm

3.2cm

year 10 lower set

9.76cm

2.18cm

year 11 lower set

8.13cm

1.63cm

Observations and conclusions:

When comparing the Higher sets to the Lower sets I can conclude that for:

- Year 7: The higher set, on average estimated closer than the lower set by 0.68cm.

- Year 8: The lower set, on average estimated closer than the higher set by 0.83cm

- Year 9: The higher set, on average estimated closer than the lower set by 0.2cm

- Year 10: The higher set, on average estimated closer than the lower set by 1.38cm

- Year 11: The lower set, on average estimated closer than the lower set by 0.03cm

From simply looking at these results I can see that the Year 8 and 11 lower set groups estimated closer on average then their years higher set. In addition, Year groups 7,9 and 10’s higher sets estimated closer on average than their lower sets. Although you would first think that Higher sets won by 3 to 2, when you look at Year 8 there is very unreliable data which I would predict their higher set to do better than the lower set due to there standard deviation. I’ve studied how different each year group sets were from one another and the closest year group were the Year 11’s. The difference between their higher and lower sets mean average was just 0.03cm. This shows how their very similar and not much different in mathematical ability to estimate. To support this, the standard deviation results show that both Year 11 sets have a compact range of estimates. This proves their mean average is accurate.

image07.png

Conclusion on investigating the variable: Intelligence

I’ve now analysed the investigations to do with intelligence fully and can conclude that when all the data are reliable and accurate, the higher sets in each year group would come out on top when compared with their year groups lower set. In my hypothesis I said that I felt experience in estimating would affect the results and I can say that this supports my prediction. Although the results show otherwise, many of the mean averages are unreliable due to their standard deviation, when taking this into account overall the intelligence of a person would affect a person’s ability to estimate. During the investigation where I compared each year groups higher and lower sets, only year 8 and 11 results showed the lower set doing better than their higher sets. For the year 8’s, the lower sets stan.dev was twice the amount of the higher sets. Finally, for year 11 the mean average was only different by 0.03cm and also their stan.dev weren’t very similar. In this case I would say the two sets were equally as good due to the lack of accuracy.

Investigating Gender

In this part of the investigation I will investigate Gender. This is to see whether being male or female means your ability in estimating is better. To begin with I’ll study male against female. Then I’ll go onto investigate different year groups with the sexes. For example I’ll look into whether being a female in year 11 means your estimating ability is better than a female in year 7. Like I’ve done in both of the other variables, age and intelligence, I will show the results in a range of different charts and graphs. This will allow the reader a better view of the results and data. As well as this I’ll be able to make observations from being able to see the data in different charts.

Comparing Male to Female

Gender has many different areas which can be covered. I’m starting off with simply comparing all the males to all the females:

        MEAN AVERAGE

 STANDARD DEVIATION

              MALE

                9.16CM

                 2.59

             FEMALE

                8.57CM

                 2.14

From this table, I can see that all females are better at estimating then all males.

In a graph I think these results would be easier to compare, therefore below is a column chart to evaluate both sets of results:

image08.png

Observations and conclusions:

- The column chart shows that the females are on average better at estimating then males. The males mean average was 9.16cm, compared to the females closer 8.57cm estimation average.

- In addition, the female’s standard deviation showed the data to be more compact than that of the Males. This supports the mean average results as the results are more reliable.

- I wasn’t surprise to see that both male and female on average had over estimated. When looking back on other tests, nearly all the averages show the groups to have over estimated.

As a conclusion, the female group have been shown to be the better at estimating. The male group neither had better mean average nor standard deviation. This emphasises how the Males results weren’t even completely accurate and still didn’t come off the better of the two sexes. From this investigation you would agree with saying that being a female affects your ability to estimate.

As a more in depth method of analysing Gender, I will investigate the results of comparing each different Year group sex. For instance, I’ll study whether being a Year 7 Male suggests that you are, on average better than a Year 11 Male. I hope to achieve some conclusive results and display them in a number of ways to show my findings.

On the following page is a table of results to do with the investigation described above:

Comparing Year group sexes

Mean average

Standard Deviation

Year 7 Male

9.84cm

3.02

Year 7 Female

8.65cm

2.74

Year 8 Male

9.05cm

2.83

Year 8 Female

8.58cm

2.56

Year 9 Male

9.13cm

2.86

Year 9 Female

8.95cm

2.09

Year 10 Male

9.61cm

2.39

Year 10 Female

8.53cm

1.43

Year 11 Male

8.15cm

1.42

Year 11 Female

8.08cm

1.73

...read more.

Conclusion

- Mean average

- Standard deviation

- Standard Deviation P

In addition to these three, I will add a final fourth calculation to view the average error between the Stan Dev results to the more accurate Stan Dev P.

Mean average

Stan Dev

Stan Dev P

Error between Stan Dev’s

Age 11

8.9cm

2.38

2.34

0.04

Age 12

9.15cm

3.01

2.97

0.04

Age 13

9.19cm

2.95

2.91

0.04

Age 14

8.97cm

2.02

2.00

0.02

Age 15

8.72cm

1.91

1.87

0.04

Age 16

7.78cm

1.09

1.06

0.03

Year 7

9.28cm

2.9

2.87

0.03

Year 8

8.8125cm

2.69

2.66

0.03

Year 9

9.035cm

2.48

2.44

0.04

Year 10

9.0675cm

2.02

1.99

0.03

Year 11

8.1125cm

1.56

1.54

0.02

Year 7 Male

9.84cm

3.02

2.94

0.08

Year 7 Female

8.65cm

2.74

2.67

0.07

Year 8 Male

9.05cm

2.83

2.79

0.04

Year 8 Female

8.58cm

2.56

2.50

0.06

Year 9 Male

9.13cm

2.86

2.79

0.07

Year 9 Female

8.95cm

2.09

2.04

0.03

Year 10 Male

9.61cm

2.39

2.33

0.06

Year 10 Female

8.53cm

1.43

1.39

0.04

Year 11 Male

8.15cm

1.42

1.38

0.04

Year 11 Female

8.08cm

1.73

1.69

0.04

Mean average

Stan Dev

Stan Dev P

Error between Stan Dev’s

Year 7 Higher set

8.94cm

3.24

3.15

0.09

Year 8 Higher set

9.58cm

2.23

2.18

0.05

Year 9 Higher set

8.94cm

1.52

1.48

0.04

Year 10 Higher set

8.38cm

1.61

1.57

0.04

Year 11 Higher set

8.10cm

1.54

1.5

0.04

Year 7 Lower set

9.62cm

2.56

2.5

0.06

Year 8 Lower set

8.05cm

2.94

2.87

0.07

Year 9 Lower set

9.14cm

3.20

3.12

0.08

Year 10 Lower set

9.76cm

2.18

2.12

0.06

Year 11 Lower set

8.13cm

1.63

1.59

0.04

Now that I have shown the results for both Stan Dev and Stan Dev P, I can prove how the most difference to the results I have investigated is 0.09cm. This was the Year 7 Higher Set. Their previous Stan Dev was 3.24, compared to their Stan Dev P of 3.15. To conclude this problem I have encountered, I can say that the issue has been resolved and no results were vitally affected by the setback.

...read more.

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