I am going to random sample the data so it is unbiased. I will use the RAN button on my calculator, which will select a number for me to use to choose which packets of crisps I am going to work with. I will do this to randomly select 4 bags of crisps from both multipacks of walkers and the co-op.
The type of data I will use is primary data, as I was involved in the collecting the data. The downside of this is that there might be a human error made, which could effect the results of this investigation. The size of my data is 8 multipacks of 12 for walkers and 8 multipacks of 12 from the co-op, which equals 192 pieces of data to work with. But after I have randomly selected the data I am going to work with I will have 60 pieces of data. This is a good amount of data to work with, as there should be at least 30 pieces of data before it is seen as statistically correct. Also it isn’t too much data to work with.
These are my results from my random sampling to choose which crisps I will use. I have 8 multipacks each containing 12 packets of crisps. I am going to use the RAN button on my calculator to choose 4 packets of 12 from Walker’s crisps then to choose 4 packets of 12 from the co-op crisps. To use the RAN button I must press the shift button first then the RAN button, then equals, then times by 8 because there are 8 packets of 12 altogether.
- SHIFT RAN= 0.537*8=4.296= packet 4
- SHIFT RAN=0.37*8=2.96= packet 3
- SHIFT RAN= 0.067*8=4.288= packet 4 but I have already selected this packet so this piece of data does not count.
- SHIFT RAN=0.865*8=6.92= packet 7
- SHIFT RAN=0.794*8=6.3852= packet 6
From this I now know that I am going to use the packets 3,4,6 and7 to get my data from the Walkers crisps.
Now I am going to choose 4 multipackts of 12 from Walker’s crisps. By using the RAN button on my calculator again.
- SHIFT RAN=0.275*8=2.2= packet 8
- SHIFT RAN=0.519*8=4.152= packet4
- SHIFT RAN=0.95*8=7.6= packet 8
- SHIFT RAN =0.851*8=6.808= packet 7
From this I now know that I am going to use the packets 2,4,7 and 8 to get my data from the CO-OP crisps.
These are my tally charts, which shows how many packets weigh what; the weight is shown in the group column.
This is my tally chart for the CO-OP crisps.
This is my tally chart for the Walker’s crisps.
I am also going to find the mid-group-value (also known as mgv for short) for both Walker’s crisps and the CO-OP crisps. This is so I can find the median.
To find the estimated median I must find the MGV for each group, I also need the frequency for each group, I already know the frequency from my tally charts. To find the MGV I have the lower number in the group plus the higher number in the group column, then divide that answer by 2.
I now times the MGV by the frequency. Then I add up all the frequency’s together to get a total frequency, then I do the same for the MGV times frequency, by adding them all up to get a total MGV times Frequency.
Now I divide the total MGV*frequency by the total frequency. Then round that answer up to 1 decimal place. This will give me my estimated mean.
CO-OP crisps.
Estimated mean = Total MGV X Freq
Total Freq
= 1175.5
48
= 24.48958333
= 24.49 (2.d.p)
Walker’s Crisps
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
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. This means that the interquartile range is:
Upper quartile – lower quartile
24.9 - 24.00
= 0.9grams.
I am now going to do a cumulative frequency graph for the weight for the Walker’s crisps. I am going to use the C.F graph to find the median for the Walker’s crisps.
From this cumulative frequency graph, I can see that the median weight for the Walker’s crisps is 25.0grams. This is the exact weight that Walker’s are saying their crisp weight. So Walker’s are not overestimating or underestimating their crisps. The upper quartile range is 25.5g. The lower quartile range is 24.8g. The interquartile range is
Interquartile range = Upper quartile-Lower quartile
25.5 - 24.8
IQR= 0.7grams
I am now going to do a Box and Whisker Plot so I can compare the median of the Walker’s crisps and the median weight of the CO-OP crisps. Also from the Box and Wicker Plot I can see if the median is closer to the upper quartile range or closer to the lower quartile range. Also the range of the middle 50% of the data, and were the box is in relation to the minimum and maximum value.
I am now going to find the Standard Deviation for both Walker’s crisps and the CO-OP crisps. I am using standard deviation so I can find out the disruption about the mean.
I am going to do a Histogram. I am doing a Histogram for both the Walker’s crisps and for the CO-OP crisps to find the modal weight for both weights of crisps. The area of each bar in a Histogram represents the frequency.
Frequency Frequency
Density Group size
CO-OP Crisps.
Walker’s Crisps.
Evaluation
My investigation I feel was successful. I had one possible outlier, which was in the Walkers crisps, which weighed 20.99g. This could have happened for many reasons. The calculations and the collection of data have been useful and informative to help me investigate whose bag of crisps advertises their weight more accurately? As I now know the estimated mean and mode, the median, the interquartile range and the standard deviation for both Walkers and the Co-op. The results of these proved that my hypothesis was correct, that walker’s crisps would be more accurate.
If I was to do this piece of coursework again I would do more research, or I would use five groups for Walkers and Co-op instead of four. Or I would have a different variety and have three sets of information not two, such as using the Walkers crisps. The Co-op crisps and ASDA crisps.
Analysis
Summary Table
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.