# How well can you estimate the length of an object?

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Introduction

MATHS GCSE

COURSEWORK

STATISTICS

BY,

REEM AL-HASSANI 10CW

Maths GCSE Coursework

How well can you estimate the length of an object?

In this coursework, I am going to investigate how well pupils can estimate length. I will ignore the estimated weight of the object as I am only investigating lengths. My hypothesis is that Year 11 is better at estimating the length of the bamboo stick than Year 7. I predict this because Year 11 will have more experience in estimating sizes than Year 7 as they are older.

Sampling

I am going to sample 50 estimates from each year because there are too many estimates and not too much time for me to investigate them in. I feel that 50 is a good amount for me to select – it’s not too small and not too large. To select this amount of data, I will use random number sampling because it is easier and more reliable. To do this, I will use the random number generator from my calculator and enter the data in the form of a table. I don’t need to assign each pupil a number as this has already been done for me on my data sheet.

Middle

1.63

113

1.54

107

1.27

82

1.70

134

1.50

49

2.00

124

1.60

37

1.50

88

1.00

14

1.50

111

1.75

110

1.35

4

1.54

64

1.50

98

1.45

80

1.36

127

1.35

155

1.90

159

1.27

59

1.60

24

1.75

148

1.80

10

1.68

160

2.14

73

1.40

84

1.28

18

1.60

30

1.52

28

1.45

54

1.90

102

1.60

21

1.60

6

1.49

20

1.54

55

1.50

33

1.50

17

1.66

121

1.80

45

1.58

I will now construct 2 grouped frequency tables – one for Year 7 and one for Year 11.

Year 7 grouped frequency table

Length (m) | Tally | Frequency | Class Width | Frequency Density (f w) |

0.75 ≤ L < 1.00 | | 1 | 0.25 | 4 |

1.00 ≤ L < 1.30 | 11 | 0.30 | 36.67 (2dp) | |

1.30 ≤ L < 1.50 | 7 | 0.20 | 35 | |

1.50 ≤ L < 1.70 | 17 | 0.20 | 85 | |

1.70 ≤ L < 1.80 | 3 | 0.10 | 30 | |

1.80 ≤ L < 2.00 | 7 | 0.20 | 35 | |

2.00 ≤ L < 2.30 | 4 | 0.30 | 13.33 (2dp) |

To find the frequency density I used the following equation:

Frequency density = Frequency

Class Width

## I will now do the same for Year 11:-

## Year 11 Grouped frequency table

Length (m) | Tally | Frequency | Class Width | Frequency Density (f w) |

1.00 ≤ L < 1.10 | 1 | 0.10 | 10 | |

1.10 ≤ L < 1.30 | 4 | 0.20 | 20 | |

1.30 ≤ L < 1.40 | 4 | 0.10 | 40 | |

1.40 ≤ L < 1.50 | 5 | 0.10 | 50 | |

1.50 ≤ L < 1.70 | 24 | 0.20 | 120 | |

1.70 ≤ L < 1.90 | 7 | 0.20 | 35 | |

1.90 ≤ L < 2.14 | 5 | 0.24 | 20.83 (2dp) |

I used the same equation to find the frequency density.

I will now draw 2 histograms from my results.

Conclusion

Evaluation

If I had a chance in the future to carry out this investigation again, there are some things I would change in order to improve it.

First of all I would use a larger sample of estimates to produce more accurate results and improve the reliability.

Secondly, I would be interested in comparing estimates of boys with girls and I could use different age groups such as compare young people with older people (OAPs for example). Also, I would not only compare Year 7 with Year 11, but compare other year groups as well.

Thirdly the data I was given is secondary, so it might have affected the results. I would collect my own primary data from our school.

Finally, for my statistical calculations I would not only find out the mean and standard deviation, but I would also find out the range and mode.

Overall I feel that the investigation went well and I am pleased with the results. There was a small problem when I was generating my random samples. One of the estimates that came up was an extreme value of 12.13 metres. I replaced this number with another one because if I had included it then my results would be distorted.

This student written piece of work is one of many that can be found in our GCSE Comparing length of words in newspapers section.

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