Distribution of the weights of two types of sweets

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Distribution of the weights of two types of sweets

The aim of this investigation is to collect data from a population and using the results estimate population parameters i.e. mean. To collect my data I am required to measure one factor of the chosen population, these factors include:

  • Heights
  • Weights
  • Pulse rates
  • Reaction times of males and females
  • Age group’s etc.

I have decided that my population will be two types of sweets and the factor that I am going to measure is the weights of each individual sweet. The two types of sweets I have decided to use are:

  • Galaxy Minstrels
  • Maltesers

When collecting my data I will have select an appropriate method to obtain the information that I require. There are two methods in which data can be collected:

  • Survey – used to determine some particular characteristic(s) of a population, usually

done through questionnaires.

  • Experiment – used to test a factor when that factor is the only variable.

The most suitable method to use to measure the weights of individual sweets is by doing an experiment.

It would be impossible to collect the weights of each sweet in the whole population a sample of the population must be taken. A suitable sample size must be chosen which will allow me to obtain reliable data in which I could draw a conclusion from. Hence, I will be using a sample size 100 of each type of sweet, as this size will be appropriate for my requirements.

To obtain a sample of 100 sweets from the whole population it is necessary to choose a practical sampling procedure. For this investigation there are two main methods that could be used:

  • Stratified sampling – This is takes the same proportion of each population group and                                 obtaining data from that proportion.
  • Random sampling – This sampling method is where every member of the population                                has an equal chance of being selected. Hence, each member                               is selected completely at random.

I will be taking a random sample. I will obtain my random sample by buying a couple of bags of Galaxy minstrels and Maltesers on different dates i.e. a few days apart, next I will mix all the Galaxy minstrels together and place them in a bag (I will do the same to the Maltesers). To select a sample of 100 sweets I will randomly pick out 100 sweets from each of the bags and weigh them individually.

Once I have obtained my data I will use it to calculate the mean and variance weights of the sweets and the standard error, using the standard error I am hoping to be able to calculate the confidence intervals of the Galaxy minstrels and the Maltesers. From this I will be able to draw suitable comparisons and a conclusion of the sweets.

Method

To obtain my data I will be doing an experiment; I will firstly take a random sample of 100 Galaxy minstrels and 100 Maltesers (as described above). I will the measure the weights of each Galaxy minstrel and Maltesers individually using weighing scales (accurate to 2 d.p) and make a record the weights.

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Results

After doing this experiment I have obtained the following weights of the sweets:

Galaxy minstrels (g):

Maltesers (g):

Mean, Variance and Standard deviation

Now that I have obtained all the weights of each individual sweet I will be able to calculate the mean, variance and standard deviation of the sample.

Mean (u)

The mean, u, is the sum of all the data values divided by the number of observations, it is a measure of the ‘average’ value of a set of data. The mean is equally influenced equally by all ...

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