# Mathematics Handling Data Coursework: How well can you estimate length?

Danielle Howells

GCSE Maths Coursework

Mathematics Handling Data Coursework:

How well can you estimate length?

Introduction

A school teacher asks two sets of students to estimate the length, in metres and to two decimal places, of a 1.58 metre long stick, held up horizontally in front of them; this is to prevent pupils from comparing the stick to the teacher’s height. 178 Year Eleven pupils and 173 Year Seven pupils are asked.

Hypothesis

I believe that the Year Eleven pupils will be more accurate in their estimation than those in Year Seven. This is because they are older, more knowledgeable at Mathematics and have also been estimating lengths for a longer amount of time than Year Sevens.

My Plan

As there are over 170 pupils in each year, I will only be using a sample of fifty pupils from each year. I will randomly select these fifty pupils, using a certain method.

I will then group my fifty data values into a grouped frequency table. This is because fifty is still a large number of lengths to be dealing with when carrying out certain calculations.

Using my random data values, first I will calculate the mean. The mean is a type of average, which represents the pupils’ accuracy at estimation. As I believe that Year Eleven’s estimations will be more accurate than the Year Seven’s, I therefore predict Year Eleven’s mean value to be close to 1.58m.

Next I will calculate the standard deviation of the two data sets. Standard deviation is the spread of data about the mean. The larger the standard deviation, the more spread out the data and the less accurate the estimations will be. Because of my hypothesis, I therefore expect Year Eleven to have a smaller standard deviation and their estimates to be closer to 1.58m.

Using my frequency table I will create a histogram. A histogram can be used to discover the percentage of estimations within a certain range of the mean. In my investigation, I predict that 50% of Year Eleven pupils will have estimates between 1.52m and 1.64m (i.e. within 6cm of the mean), compared with 30% of Year Seven’s.

Sampling Data

I will first collect my random sample of fifty pupils, as it would be too difficult to work with over 170 pupils in each year group. My sample will be calculated using the method of random sampling. Random sampling is a method that will ensure all pupils have a chance of being chosen. There are a few ways of obtaining a random sample.

I will be using the RAN # key on my calculator to generate my random numbers. The number generated will be a decimal number between 0.0 and 0.9. I will then multiply this number by the number of pupils in each year – 173 in Year Seven and 178 in Year Eleven. I will then round this number to a whole number and this number will have represents the pupil numbers given on the data sheet.

Example – RAN # = 0.511

0.511 x 173 = 88.403

= Pupil No. 88 in Year 7

RAN # = 0.417

0.417 x 178 = 74.226

= Pupil No. 74 in Year 11

I will repeat this method fifty times on each year group in order to obtain my fifty random samples in total. Each time I find a pupil number I will circle its corresponding length. If the same pupil number comes up twice then I will disregard this number as it has already been used once. I will generate another random number instead.

Rogue values are implausible estimates that do not follow the natural pattern of the other results. In my investigation, rogue value will count as any values less than (but not including) 1.00m and any over (but not including) 2.00m. I will not include these values as they could greatly affect my final calculations such as the mean and standard deviation.

I am now going to calculate and record my fifty numbers for each year group. Below are my two tables of lengths.

In my Year Seven data set I found two rogue values (11.75m and 12.13m). I disregarded ...