1. Numeracy & Quantitative Methods: Numeracy for Professional Purposes Laura Lake

2. WHY? Just looked at measures of dispersion. The mean and standard deviation based on a normal shaped distribution Lots of values near the top or bottom of the data (presence of extreme values) then median might be better. Therefore, knowing what your data looks like can help you to make accurate decisions in the choice of statistic to use. Shape of a distribution

3. Two measures used to indicate the shape of a distribution of an interval or ratio variable: skewness kurtosis The shape of the distribution is the shape of the data when it is presented in a histogram or the trend line when plotted on a line graph. Shape of a distribution

4. First of all, what does a normal distribution look like? If all values in a data set are equally distributed then the shape will be symmetrical. A normal distribution Mean n a) Normal distribution

5. Data sets with a greater number of values at either the high or low end result in a skewed distribution shape. Calculating the skewness will indicate the position of the lower and higher values in a data set which pull the shape of the distribution towards the lower or higher end. If the data has a large number of low values then the shape will be positively skewed. If the data has a large number of high values then the shape will be negatively skewed. Skewness in a distribution

6. Skewed distributions Mean Exam score: biology b) Negatively skewed distribution Median

7. Skewed distributions Mean c) Positively skewed distribution Median Exam score: chemistry

8. Kurtosis looks at how the values in a data set are distributed around the mode. Types of kurtosis: positive kurtosis – leptokurtic (“peaky”) negative kurtosis – platykurtic (“flat”) even distribution is mesokurtic Kurtosis

9. Positive kurtosis n a) Positive kurtosis

10. Negative kurtosis n b) Negative kurtosis

11. To understand the distribution of a variable: examine the shape of the distribution ( a histogram or line graph trend line) given the shape, examine the data with the most suitable methods examine how far away the data is from a normal distribution Different evidence helps to build a picture of understanding. Summary

12. Bryman, A. (2008) Social Research Methods. 3rd Ed. Oxford: Oxford University Press. David, M. and Sutton, C. (2011) Social Research : An Introduction. 2nd ed. London: Sage. References

13. This resource was created by the University of Plymouth, Learning from WOeRk project. This project is funded by HEFCE as part of the HEA/JISC OER release programme.Learning from WOeRk This resource is licensed under the terms of the Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales license (http://creativecommons.org/licenses/by-nc-sa/2.0/uk/).http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ The resource, where specified below, contains other 3 rd party materials under their own licenses. The licenses and attributions are outlined below: 1.The name of the University of Plymouth and its logos are unregistered trade marks of the University. The University reserves all rights to these items beyond their inclusion in these CC resources. 2.The JISC logo, the and the logo of the Higher Education Academy are licensed under the terms of the Creative Commons Attribution -non-commercial-No Derivative Works 2.0 UK England & Wales license. All reproductions must comply with the terms of that license. Author Laura Lake InstituteUniversity of Plymouth Title Numeracy & Quantitative Methods Numeracy for Professional Purposes Description Basic Descriptive Statistics: Introduction Date Created May 2011 Educational Level Level 4 Keywords Learning from WOeRK Work Based Learning WBL Continuous Professional Development CPD Research UKOER LFWOER Skewness, kurtosis, leptokurtic, platykurtic, mesokurtic. Back page originally developed by the OER phase 1 C-Change project ©University of Plymouth, 2010, some rights reserved