What Can Statistics Be Used For?

What Can Statistics Be Used For? exercise

• What can statistics be used for?

  Hints

  Statistics is a science which looks at data.

  For that to happen it needs to be collected first.

  When you have collected your data, you need to be able to present it so you can understand what it is telling you.

  Look at the other words which support this.

  There are $4$ correct answers.

  Solution

  • Collecting data
  • Analysing data
  • Organising data
  • Interpreting data

  This is the statistics cycle.

• Why collect a sample?

  Hints

  The "population" is the total amount of people in a survey.

  For example, if we wanted to ask the whole school a question then the school would be the population.

  A sample can be taken instead. Which is a cross section of the students who would represent the whole population.

  If we only ask a sample we would save a number of things.

  Here is a picture clue to some of the answers missing above.

  • Saves money - it is cheaper.
  • Saves time - it is quicker.

  Solution

  Using a sample instead of asking the opinion of the whole population has a number of advantages. Firstly, it is cheaper as it does not cost as much to ask a sample.

  It saves time asking a sample, as it would take longer to ask everyone in the population. To ask everyone, we would need to employ more staff which would also cost more.

• What size should the sample be?

  Hints

  A random sample has to be representative of the population of $800$.

  Not too many, as Tommy could have asked the whole school.

  To be representative of the school there has to be enough people asked in order to reflect this.

  A good example of a sample size would be around $10$ out of a population of $50$, or $200$ out of $1000$.

  Approximately $20$% of the population is a good estimate for a sample size.

  Solution

  $\mathbf{100}$

  This is a good number to use as a sample.

  $5$ and $10$ is much too small and $600$ is nearly the whole population.

• How do we use statistics?

  Hints

  • We start by collecting data
  • We get this by surveys, questionnaires etc.
  • This data collected should then be organised into a readable format.

  • Questionnaires to collect the data
  • Organise into a spreadsheet
  • Next comes the analysing and interpreting.

  The very last part of this is interpreting the data you have collected to see if it supports your initial theory.

  Solution

  Collecting - Send out questionnaires.

  Organising - Enter data into a spreadsheet and put into a graph.

  Analysing - Check out the results that the data is showing.

  Interpreting - Finally, do these results help prove what we were looking for, or otherwise?

• Using graphs to organise data.

  Hints

  Each way of organising data does what it says in the title.

  For example, a pie chart is circular and looks like a pie.

  A bar chart has multiple bars to represent the data and a line graph uses lines.

  A scatter graph has data points which look like they have been scattered on the axes.

  Solution

  Here we can see the graphs alongside their correct names.

• What is a random sample?

  Hints

  A random sample is a representative sample where everyone has an equal chance of being chosen.

  A random sample can be generated by a calculator, a computer or numbers can be picked out from a hat.

  Everyone has to have an equal chance!

  There are three correct answers here.

  Solution

  Doug gives every address in the town a number and generates random numbers using his computer.

  Doug uses postcodes and the computer sends out surveys to random addresses.

  Doug uses the names of all the people in the town from the town hall census. He randomly generates the sample names to ask.

  • If Doug asks his family or football team mates that is biased.
  • If Doug asks the whole town that is not a sample but the "population".
  • If Doug stands outside the supermarket he would not be giving everyone in the town an equal chance of being picked.
  • If Doug uses the old list of people from $2001$, some of them could have moved or died and others may have been born.