Measures of central tendency and dispersion

Measures of central tendency Mean Median Mode ie finding a ‘typical’ value from the middle of the data.

You need to be able to: Explain how to calculate the mean, median and mode State the strengths and weaknesses of mean, median and mode This could include saying which one you would use for some data e.g. 2, 2, 3, 2, 3, 2, 3, 2, 97 - would you use mean or median here?

Advantages and disadvantages  MeanMore sensitive than the median, because it makes use of all the values of the data. It can be misrepresentative if there is an extreme value. MedianIt is not affected by extreme scores, so can give a representative value. It is less sensitive than the mean, as it does not take into account all of the values. ModeIt is useful when the data are in categories, such as the number of babies who are securely attached. It is not a useful way of describing data when there are several modes.

Measures of Dispersion Measures of ‘spread’ This looks at how ‘spread out’ the data are. Are the scores similar to each other (closely clustered), or quite spread out?

Range and standard deviation The range is the difference between the highest and lowest numbers. What is the range of … 3, 5, 8, 8, 9, 10, 12, 12, 13, 15 Mean = 9.5range = 12 (3 to 15) 1, 5, 8, 8, 9, 10, 12, 12, 13, 17 Mean = 9.5range = 16 (1 to 17) Example from Cara Flanagan, Research Methods for AQA A Psychology (2005) Nelson Thornes p 15

Standard deviation Standard deviation tells us the average distance of each score from the mean. 68% of normally distributed data is within 1 sd each side of the mean 95% within 2 sd Almost all is within 3 sd

Example Mean IQ = 100, sd = 15 What is the IQ of 68% of population (ie what is the range of possible IQs)? Between what IQ scores would 95% of people be? Dan says he has done an online IQ test, and he has an IQ of 170. Should you believe him? Why/not?

Another example Sol scores 61% in the test. His mum says that’s rubbish. Sol points out that the mean score in class was 50%, with an sd of 5. Did he do well? What if the sd was only 2? What if sd was 15?

Advantages and disadvantages AdvantagesDisadvantages RangeQuick and easy to calculateAffected by extreme values (outliers) Does not take into account all the values Standard deviationMore precise measure of dispersion because all values are taken into account Much harder to calculate than the range I used Cara Flanagan’s (2005) Research Methods for AQA A Psychology Nelson Thornes in preparing these slides.