• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12

Descriptive Statistics 1. Mean, median and mode.

Extracts from this document...


Descriptive Statistics 1. Mean, median and mode.


At this stage I want to emphasize the practical relevance of averaging, using the discussion of the mean to illustrate the use of mathematical notation (that was introduced last week), and warn you about some of the possible pitfalls of relying on the average without looking at the pattern of values from which it was calculated. First, however, I will attempt to answer the good question, “why bother learning statistical notation”, that seems to crop up every year.

Why learn mathematical notation?

PSY107 aims to provide not just a recipe book for doing statistics problems in isolation, but aims to leave you with some skills that have general relevance. These include computer literacy, the ability to explore data, critical thinking, and a degree of independence in tackling statistical issues in Psychology and elsewhere. The routine tools that I and many of my colleagues use to do statistics are not algebra and equations, but (often computerized) graphing and data analysis methods. I think that many simple statistical concepts can be communicated using graphs and plain English. Why, if many psychologists do not spend their time writing μ and σ is it necessary to get to grips with the basics of statistical notation?

This question has several answers. First, mathematical language is logical, rigorous, and compact. Mathematical notation can also be used to represent the precise relationship between different statistical concepts.

...read more.


Definition of the mean

The arithmetic mean is the sum of the values divided by the number of values. This is shown below using mathematical notation. It is best to get to grips with the symbols while the statistical concepts they represent (e.g. mean average) are simple and familiar.

Sample mean vs. population mean

μ, the population mean, is the mean derived from the entire population under study. Population is a word with a somewhat elastic meaning, but generally it is up to you, the experimenter, to define your population. It might be all the people in the UK, all the people who shop at KwikSave, or all the lecturers in the Newcastle University Psychology Department. With large populations, it is often impractical to find μ.


image02.png, the sample mean, is calculated from a representative sample of the population. This is usually done by selecting individuals from the population at random to avoid sampling bias. You get sampling bias when all the members of the population under study do not stand an equal chance of being measured.


If you wanted to estimate the mean height of people in the UK, it would be stupid to do all your measuring in primary schools. This is an extreme example, but more realistically, suppose you wanted to get a representative 1000 people to complete a questionnaire on social attitudes. If you did the survey by telephone, your sample would be biased towards telephone owners. If you called between 9 and 5, your sample would be biased towards people without day jobs.

...read more.


The Median.

The median is the value that divides the distribution of values exactly in half. To find the median, sort or rank the values and find the middle value (if there are is an odd number of values) or else the mean of the central two values (if there is an even number of values). It is possible to estimate the median from histograms. Use the information on number of scores to estimate the position of the middle score.

Fig. 7


Estimate the position of the “middle person” on the income axis using the information on the frequency axis. Here there are 18 lecturers, so the median income is at the estimated position between 9 and 10. This is simpler to estimate from a cumulative frequency polygon.

The median average can be more representative than the mean in skewed distributions (e.g. annual income, or National Lottery winnings). Remember to look at the data when you calculate the median average

Fig. 8


The Mode

The mode is the score or category that has the greatest frequency. The modal average can be used with nominal data. As with all other averages, look at the data when you calculate the mode.

Fig. 9


Is a three dimensional representation sensible?

Mike Cox


Version 1

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. The mathematical genii apply their Statistical Wizardry to Basketball

    Same arms used each time. * The weather conditions being similar. In the sports hall there should be no significant alteration of the environment. * Each shot being taken one after the other to gain results, which will be under the most similar conditions.

  2. Used Cars - What main factor that affects the price of a second hand ...

    2000 23294 2 8999 38 LARGE 2000 13130 1 10699 39 LARGE 2000 25520 4 5699 40 LARGE 2000 27420 1 18199 41 LARGE 2000 12879 1 11299 42 LARGE 2000 14345 2 14999 43 LARGE 2000 23490 3 6999 44 LARGE 2200 23050 2 19699 45 LARGE 2200 11120

  1. Estimating the length of a line and the size of an angle.

    11, which are female Now I will work out the sample size for each group (males and females) of each quarter for year 11. I will do this by using the same method as I did to work out the sample size for year 10.

  2. find out if there is a connection between people's IQ and their average KS2 ...

    If you notice on my graph there are points that do not fit in with any of the others. One person had a high SATs Result but a very low IQ; the other person had a low SATs result but a very high IQ. These two points are called outliers.

  1. I want to find out if there is a connection between people's IQ and ...

    A scatter graph would be best as it would be easier and clearer for me to see any connections and the correlation of the IQ and the average KS2 SATs results. Microsoft Excel drew my graph for me quickly and accurately on the computer.

  2. Fantasy Football - Maths Coursework - Statistics

    You get 5 points for each goal and an extra 5 points if you score 3 or more goals. I think that attackers will also score more because unless they are booked during the game, there is no way for them to loose points, unlike defenders who loose points for conceding goals.

  1. Case study -Super Savers is wishing to move into the UK Food Retail market.

    of the sensory profile * To find out which attributes most affect consumer acceptance * To discover which product consumers prefer 4.METHODOLOGY Experimental Design The initial step in this process is to develop a written plan, reflecting what has to be done, what is being done now, and what could be done in the future.

  2. Teenagers and Computers Data And Statistics Project

    3 1 6 [ (n - 2) 2] 2 12( n-2) 3 8 Total n 3 7. The 10 x 10 x 10 table Number of red faces Number of cubes 0 512 1 384 2 96 3 8 4 0 5 0 6 1000 Total 8.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work