# Estimates of a straight line and a curved line

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Introduction

1 Y10 GCSE Statistics Investigation

Introduction:

The subject I have decided to carry out is an assignment on estimates of a straight line and a curved line. I am going to find out if there is any relationship between the estimates of a straight line and a curved line.

Aims:

My aims are as follows

- If you estimate a curved line accurately do you also estimate a straight line correctly?
- Are half of all estimates within 10% of the actual measurement?
- Do Y10 students have a greater number of pupils within 20% of the median than Y7 pupils?
- To find out who is better at estimating straight lines, girls or boys?

I am going to answer these questions in my investigation by using the information I gather and the diagrams I formulate, when the aims are found I will then analyse the results.

Planning:

I am going to look at the recordings taken from Y7 and Y10, boys and girls. The two factors I am going to investigate are age and gender and their ability to estimate a straight line and a curved line.

Middle

% error

Rank of curved line

Rank of straight line

d

d

0

2.5

3.5

1

1

0

5.5

3.5

2

4

8

15

10

5

25

-92

24.5

25

0.5

0.25

0

17

3.5

13.5

182.25

0

5.5

3.5

2

4

-8

5.5

10

4.5

20.25

23

17

20.5

3.5

12.25

23

21

20.5

0.5

0.25

23

22.5

20.5

2

4

8

8

10

2

4

15

13.5

15.5

2

4

-31

13.5

24

10.5

110.25

0

1

3.5

2.5

6.25

-23

19.5

20.5

1

1

-8

2.5

10

7.5

56.25

-15

10

15.5

5.5

30.25

-8

12

10

2

361

-8

5.5

10

4.5

30.25

0

22.5

3.5

19

12.25

-15

10

15.5

5.5

16

23

17

20.5

3.5

0

-15

19.5

15.5

4

16

8

10

10

0

-23

24.5

20.5

4

9.25

Spearman’s Rank = 1-6 d /n(n -1) = 1-6*925/25 (25 -1) = 1-5550/15600=1-0.35576923=0.644230769

Girls error | |||

Curved line=38 | Straight line=13 | ||

Curved line estimate | % error | Straight line estimate | % error |

37 | 3 | 11 | 15 |

40 | -5 | 10 | 23 |

24 | 37 | 15 | -15 |

32 | 16 | 14 | -8 |

44 | -16 | 20 | -54 |

35 | 8 | 12.5 | 4 |

100 | -163 | 10 | 23 |

30 | 21 | 18 | -38 |

21 | 44 | 12.5 | 4 |

28 | 26 | 11 | 15 |

24 | 37 | 14 | -8 |

35 | 8 | 10 | 23 |

34 | 11 | 13 | 0 |

32 | 16 | 11 | 15 |

28 | 26 | 16 | -23 |

35 | 8 | 10 | 23 |

34 | 11 | 10.5 | 19 |

50 | -32 | 13 | 0 |

40 | -5 | 12 | 8 |

36 | 5 | 15 | -15 |

49 | -29 | 16 | -23 |

43 | -13 | 16 | -23 |

40 |

Conclusion

-1

1

8.5

19.5

-11

121

11.5

15

-3.5

12.25

21

1.5

19.5

380.25

4.5

6

-1.5

2.25

4.5

11

-6.5

42.25

20

19.5

0.5

0.25

13

19.5

-6.5

42.25

4.5

11

-6.5

42.25

8.5

11

-2.5

6.25

1

19.5

-18.5

342.25

total=2701.5

Spearman’s rank = 1-6 d /n(n -1)=1-6*2701.5/25(25 -1)=1-16209/15600=1-1.039038461

From these two pieces of information I can see that there is a strong positive correlation in boys estimates and no correlation in girls estimates. This tells me that boys, when they estimate either curved or straight line accurately, they also estimate the other accurately aswell. With girls this doesn’t happen. When girls estimate one line accurately, they usually estimate the other line badly.

Q2

When the pupils estimate the curved line, do boys and girls in y10 have a greater number of pupils with 20% of the median than Y7’s. I will have to work the % error for both Y10 and Y7’s.

Curved line estimate | % error | Y7 B+G | Curved line estimate | % error |

44 | 16 | 3 | 37 | 3 |

38 | 0 | 0 | 36 | 5 |

50 | 32 | 5 | 31 | 18 |

39 | 3 | 0 | 60 | 58 |

35 | 8 | 7 | 30 | 21 |

34 | 11 | 0 | 40 | 5 |

40 | 5 | 3 | 36 | 5 |

56 | 45 | 1 | 30 | 21 |

35 | 8 | 1 | 24 | 37 |

30 | 21 | 3 | 21 | 45 |

50 | 32 | 2 | 35.5 | 7 |

35 | 8 | 0 | 44 | 16 |

60 | 58 | 0 | 37 | 3 |

34 | 11 | 0 | 40 | 5 |

32 | 16 | 0 | 24 | 37 |

28 | 26 | 0 | 32 | 16 |

35 | 8 | 2 | 44 | 16 |

34 | 11 | 0 | 35 | 8 |

50 | 32 | 0 | 100 | 163 |

40 | 5 | 0 | 3 | 21 |

36 | 5 | 0 | 21 | 54 |

49 | 29 | 0 | 28 | 26 |

43 | 13 | 3 | 24 | 37 |

40 | 5 | 0 | 35 | 8 |

35 | 8 | 2 | 23 | 56 |

38 | 0 | 5 | 41 | 7 |

I will then have to group the pieces of data to make a cumulative frequency diagram.

Group | Y10 Freq | Y7 Freq | Y10 Cumulative frequency | Y7 Cumulative Frequency |

0--4 | 3 | 2 | 3 | 2 |

5--9 | 9 | 6 | 12 | 8 |

10--14 | 4 | 0 | 16 | 8 |

15--19 | 2 | 4 | 18 | 12 |

20--24 | 1 | 3 | 19 | 15 |

25--29 | 2 | 1 | 21 | 16 |

30--34 | 3 | 0 | 24 | 16 |

35--39 | 0 | 3 | 24 | 19 |

40--44 | 1 | 0 | 25 | 19 |

45--49 | 0 | 1 | 25 | 21 |

50--54 | 0 | 1 | 25 | 22 |

55--59 | 1 | 1 | 26 | 23 |

60--64 | 0 | 0 | 26 | 23 |

65--69 | 0 | 0 | 26 | 23 |

70--74 | 0 | 0 | 26 | 23 |

75--89 | 0 | 0 | 26 | 23 |

90--94 | 0 | 0 | 26 | 23 |

95--99 | 0 | 0 | 26 | 23 |

100--104 | 0 | 0 | 26 | 23 |

105--109 | 0 | 0 | 26 | 23 |

110--114 | 0 | 0 | 26 | 23 |

115--169 | 0 | 0 | 26 | 24 |

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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