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• Level: GCSE
• Subject: Maths
• Word count: 4247

Extracts from this document...

Introduction

Yr11 GCSE Statistical Math’s Coursework 2001

Aim

Prediction

My hypothesis is that adults are more accurate estimators than children because they have a more educated mind that enables them to have a far greater understanding of a problem than a child would.

Plan

I firstly need to design a series of tests making people use their own way to estimate something. I will use four different estimation tests.  Once that I have decided upon the themes of the test and have measured them out as accurately as possible I will need to set up groups of people that fit into the category of adult or child. I have decided to use two groups to test the proposition. In consideration of adults by law, you are legally an adult at 18 years of age so my first group consists of 18+’s. My second band will consist of teenagers of 13 to 17 year olds. In each group, I will test 20 people: 10 males and 10 females (or boys and girls). This will allow me to understand whether sex is another factor I have to consider when looking at the difference in estimations. This gives me a total of 40 results.

I am not going to use any child below the age of thirteen as I think they will find it more difficult to understand the problem. The groups and group sizes will give me a good line of data that I can interpret and use to understand the aim and to answer the question.

For the estimator to estimate accurately there are some key factors that he or she should have, they are:

• Intelligence – the ability to work something out
• Experience – relating to another measurement (to have the knowledge of the measurement)
• Concentration
• Understanding of the problem
• Methodology – ability to work out how to estimate something

Middle

17

270

Jenny

Female

16

200

Gemma

Female

15

300

Jess

Female

15

220

Kate

Female

14

786

Sophie

Female

14

235

Jane

Female

13

290

Kelly

Female

13

255

Sarah

Female

13

190

MEAN

14.5

303

MODE

14

200

RANGE

17-13= 4

1503-120= 1383

Median

14

220

After looking at the results of the teenagers estimations, it was interesting to see how far the majority were away from the actual weight of 300 grammes. Only three estimators were 30 grammes away from the 300 grammes, they were Jane, Gemma and Natalie.  It is interesting to see that all three are girls, perhaps because they are more familiar with cookery ingredient weights.  The guess that took me totally by surprise was that of Charlie, who got 1503 grammes.  This is such an over estimation (it is 1203 grammes from the actual weight of 300 grammes) but she based it on cooking weights and therefore should have been a reasonably accurate estimation.  Everyone compared the weight with the coffee and seemed to think the flour weighed less than the coffee, this may be down to the fact that they could not see the coffee in the bag whereas they could see the flour.

 Name Sex Age Estimations  (grammes) Greg Male 44 803 Ian Male 43 280 Richard Male 40 255 John Male 34 400 Neil Male 30 290 Tony Male 24 310 Andy Male 21 320 Eric Male 19 350 Dean Male 18 260 Sam Male 18 225 Ester Female 44 120 Liz Female 42 280 Gwynne Female 40 116 Kerry Female 39 350 Linda Female 39 289 Debbie Female 34 150 Sarah Female 21 349 Hannah Female 20 400 Jo Female 19 390 Laura Female 18 320 MEAN 30 312.85 MODE 18 NA RANGE 44-18= 26 803-116= 687 Median 30 290

It is unsuitable for me to use a mode as I had quite a few numbers with the same frequency.  Although the mean is not as close to the actual weight as the teenagers one is, this is because of one of the teenage results is very high (1503 grammes) and so helped to create a closer mean.  That this is the case is indicated by the adult range and median, which are both closer to the actual weight.  Seven adult estimators had good results, within 30grammes of the actual weight of 300 grammes.  They were Ian, Greg, Neil, Tony, Liz, Laura and Linda. Interestingly enough more males are closer than females where as in the teenage results the females were closer.  This shows that as men get older they are more likely to get a better estimation than women are.  Gwynne got a bad estimation because she did not use the coffee to her advantage; she did not hold the coffee and the flour in different hands like a set of scales so she was not very accurate.  Neil used his hands as weighing scales and got an extremely accurate result, however no adult got the weight spot on like the teenager Gemma did.

I have produced two lots of graphs (following this page) that show the results in the table above.  I notice on the adult pie chart half the results fall between 116-300 grammes whereas on the teenage one (children written at the top of the page) 55% of the results fall between 100-220 grammes.  This reveals a lower set of estimates than that for the adults.  On the pie and bar charts 30% of results lie between 301 and 350 for the adults. This is far closer to the actual weight than the most popular weight range for the teenagers (25% between 191-220 grammes).  It is interesting to see that there are no results in the range 181-210 for adults but for the teenagers the biggest amount can be found in the two bars on their bar chart.  This shows that teenagers are more likely to estimate the weight of something below its actual weight but adults are more likely to estimate the weight above but close to the actual weight.

I therefore conclude that for Test 2, the adult results are more accurate than those of the teenagers are.

Test 3 is a quantity estimation test, involving looking at a bag of conkers for a short period of time (10 seconds) and estimating the number in the bag.  The bag is see-through and I do not have any specification to use the same sized conkers.  I will not be letting people touch the bag to feel the conkers or to estimate the weight as this may effect their estimations. There were 23 conkers in the bag.   I used 23 conkers as it was an odd number and I wanted to see if people were more likely to estimate odd or even numbers.

 Name Sex Age Estimations Gregg Male 44 50 Ian Male 43 22 Richard Male 40 18 John Male 34 29 Neil Male 30 24 Tony Male 24 22 Andy Male 21 22 Eric Male 19 22 Dean Male 18 21 Sam Male 18 22 Ester Female 44 21 Liz Female 42 18 Gwynne Female 40 24 Kerry Female 39 40 Linda Female 39 19 Debbie Female 34 30 Sarah Female 21 27 Hannah Female 20 23 Jo Female 19 31 Laura Female 18 27 MEAN 30 25.6 MODE 18 22 RANGE 44-18= 26 50-18= 32 Median 30 22

Conclusion

One interesting observation is that in three out of four tests the teenager mean was closer to the actual measurement than that of the adults.  However, by using the more sophisticated statistical analysis methods, I have demonstrated the adults to be more accurate as a group.

My results are partly from people I know and partly from people I do not know. The people I know have good educations and are from well brought up backgrounds, which could affect the way they estimate. It might make them more accurate because they have more information on how to estimate more accurately than the estimators I don’t know have a well-educated background. I could have got results that are more reliable simply by getting people in a public place on everyday of the week at different times to do my test and not to let people I know do the tests.

I made sure every part of my test was fair, I went through each test checking and re-checking that it was as it should be. I made sure no one knew any of the results and that people didn’t look on as an estimator estimated something. All my workings are double-checked and some had to be changed once I had made a second check. I made sure that my tests were fair.

My data suggests that the estimations made by adults are more accurate than the estimations made by teenagers. A practical use for this would be to employ adults that are good at estimating in a trucking firm. They could look at the speed of the trucks and the distance each truck has to travel and estimate how many trips a truck can make in a certain amount of time. That person could estimate the amount of fuel needed and how many stops the truck driver will need to take for a decent rest. A good estimator would be very useful in a job like this.

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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