# USP493 Session 3 Notes

- Graphic presentation of data
- For nominal and ordinal data you can do a pie chart or a bar chart
- For grouped interval data you can construct a histogram
- For grouped or ungrouped interval data you can construct line graphs

- Measures of Central Tendency
- Mode – can be used for nominal, ordinal and interval data the most often selected value (Note the mode is the value of the variable not the frequency) can have a bimodal distribution when more than two modes
- Median – can be used for ordinal and interval data the “middle” value – half the sample is higher and half lower
- line up all the cases from the smallest to the largest
- find the middle position (N+1)/2
- if odd number of cases, it will be the value of that case
- if even number of cases, it will be the average of the values of the cases on either side of it. For ordinal data, simply state it is between the two values.
- Locating a median if you have a cumulative frequency distribution

- The mean – can be used for interval data
- calculating a mean from a frequency distribution
- multiple the number of cases which take on each value by the value, then add together and divide by the number of cases as usual

- Relationship between mode, median and mean
- Which one should you use?
- The shape of a distribution
- Symmetrical – mean median and more are the same
- Positive skew – there are some extreme high values
- Negative skew – there are some extreme low values

- Measures of Variability
- Index of Qualitative Variability – used for nominal data
- The range – used for interval data – simply the largest value minus the lowest value. The interquartile range, the difference between the cutpoint where 25 percent of the cases have a larger values, and the cutpoint where 25 percent of the cases have a lower value. The boxplot shows the range, the interquartile range and the median
- The variance and standard deviation, a measure of the amount scores cluster at the mean or spread out from the mean. Used for interval data. The variance is the average squared deviation of scores from the mean. The standard deviation is calculated from the variance. You simply take the square root of the variance.