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  • Level: GCSE
  • Subject: Maths
  • Word count: 3039

Investigate weather or not the co-op or walkers crisps advertise their weight more accurately.

Extracts from this document...

Introduction

Krystina Henderson

Maths Coursework-Statistics

Introduction

        This piece of coursework is my statistics coursework. For this piece of coursework I will be investigating weather or not the co-op or walkers crisps advertise their weight more accurately. Their advertised weight is 25grams.

Hypothesis

        For my hypothesis I predict that the walkers crisps will be more accurate to their advertised weight of 25grams, than the co-op crisps who’s advertised weight is also 25grams. I predict this because walkers are a bigger manufacturer and therefore I think they will try harder to be truer to the ideal weight.  

Plan

        For this piece of this coursework I will be collecting data, to collect the data I will use cluster sampling to collect the data on the weight of all the crisps, and to find the weight of a empty packet of crisp. I will use random sampling to choose which pieces of data I am going to use. I will be using cluster sampling and random sampling to make sure the data is unbiased.

I am going to group the data because I feel it will be easier to work with if I group it, as I have a lot of data to work with.

...read more.

Middle

27.50≤w<28.00

0

27.75

0

Total

48

Total

1175.5

                Estimated mean = Total MGV X Freq

                                                       Total Freq

                                           = 1175.5

                                                         48

                                                    = 24.48958333

                                                    = 24.49 (2.d.p)

Walker’s Crisps

Group

Freq

MGV

MGV X Freq

20.50≤w<21.00

1

20.75

20.75

21.00≤w<21.50

0

21.25

0

21.50≤w<22.00

0

21.75

0

22.00≤w<22.50

0

22.25

0

22.50≤w<23.00

0

22.75

0

23.00≤w<23.50

0

23.25

0

23.50≤w<24.00

0

23.75

0

24.00≤w<24.50

3

24.25

72.75

24.50≤w<25.00

13

24.75

321.75

25.00≤w<25.50

18

25.25

454.5

25.50≤w<26.00

9

25.75

231.75

26.00≤w<26.50

2

26.25

52.5

26.50≤w<27.00

1

26.75

26.75

27.00≤w<27.50

0

27.25

0

27.50≤w<28.00

1

27.75

27.75

Total

48

Total

1208.5

                 Estimated mean = Total MGV X Freq

                                                          Total Freq

                                          = 1208.5                        

                                          48

                                  = 25.17708333

                                            = 25.18 (2.d.p)

I am now going to do a cumulative frequency graph also known as a c.f. graph. I am using this because I want to find the median for both the CO-OP crisps and the Walker’s crisps.

CO-OP Crisps

Group

Frequency

22.00≤w<22.50

1

22.50≤w<23.00

1

23.00≤w<23.50

2

23.50≤w<24.00

7

24.00≤w<24.50

10

24.50≤w<25.00

17

25.00≤w<25.50

7

25.50≤w<26.00

2

26.00≤w<26.50

1

26.50≤w<27.00

0

27.00≤w<27.50

0

27.50≤w<28.00

0

Group

C.F

22.00≤w<22.50

1

22.50≤w<23.00

2

23.00≤w<23.50

4

23.50≤w<24.00

11

24.00≤w<24.50

21

24.50≤w<25.00

38

25.00≤w<25.50

45

25.50≤w<26.00

47

26.00≤w<26.50

48

26.50≤w<27.00

48

27.00≤w<27.50

48

27.50≤w<28.00

48

From this cumulative frequency graph I can see that the median weight for the CO-OP crisps is 24.6grams. This is lower than the advertised weight, which means the CO-OP are overestimating the weight of their crisps by an average of 0.4g, but this could still make a big difference! The upper-quartile range is 24.9, and the lower quartile range is 24.00g.

...read more.

Conclusion

Analysis

Summary Table

Walker’s

Co-op

Estimated mean

25.18 (2.d.p)

24.49 (2.d.p)

Estimated mode

25.2

24.7

Median

25

24.6

Interquartile range

0.7

0.9

Standard Deviation

0.8

0.7

My data shows that the Walkers estimated mean is 25.12 as this is over 25 it suggest that walkers are overestimating the weight of their crisps while the Co-op estimated mean is 24.49 which suggest the opposite they are underestimating the weight of their crisps. The estimated mode for walkers is 25.2 and the estimated mode for Co-op is 24.7, which again suggest walkers are overestimating and the Co-op is underestimating the weight of their crisps.

        All this data suggest that my hypothesis is correct. As Walkers crisps are truer to their advertised weight and there is extra in their crisps as well. From my data it seems that the Co-op underestimate the weight of their crisps.

         The factors that could have effected my results would be any outliers, or incorrect readings.

This is my result from my standard deviation for the Co-op crisps.

Co-op

Standard deviation = 0.772211260  - 0.77(2.d.p)

Mean                     = 24.0445625   - 24.04

This is my result from my standard deviation for the Walkers crisps.

Walkers crisps

Standard deviation = 0.853581466  - 0.85(2.d.p)

Mean                     = 25.18288462 – 25.18 (2.d.p)

I am now going to show the results of my Standard deviation on a table.

...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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