DS5 CEC Interpreting Sets of Data

Measures of Location: mean and median Measures of location, sometimes called measures of central tendency, are single numbers used to represent or summarise a set of data. For the scores 5, 5, 6, 6, 7, 7, 7, 9 calculate the mean. Find the median for these scores. 2, 3, 4, 4, 6, 7, 7

Measures of Location: mode The mode is the score that occurs the most. It is the score with the highest frequency. The mode is useful for categorical data that do not allow numerical calculations. e.g. Find the mode of the set: 1,2,3,3,3,4,5,6 The mode is 3, as it occurs most often

Measures of spread: The following sets of marks both have the same mean of 10. Set A: 8, 9, 10, 11, 12 Set B: 0, 1, 10, 19, 20 In set A, the scores are within 2 marks of the mean. In set B, the scores are spread up to 10 marks away from the mean. Hence, as well as having a central representative value for a data set, it is also useful to have a measure of the spread of the data. Such measures of spread are called measures of dispersion. The measures of dispersion we investigate in this course are the range, interquartile range and standard deviation. The standard deviation is found using the calculator ( )

Interquartile Range • 25% of the scores are less than Q1, the lower quartile, and 75% are greater than it. • 50% of the scores are less than Q2, the median, and 50% are greater than it. • 75% of the scores are less than Q3, the upper quartile, and 25% are greater than it. To divide data into quartiles, divide the ordered set into four equal sections (like finding the median and then finding the median of each half of the data). e.g. Find the interquartile ranges (IQR) of these scores. 3, 3, 4, 5, 5, 6, 6, 6, 8

Displaying two sets of Data Stem-and-leaf plots, box-and-whisker plots, and radar charts are used to compare two sets of data. e.g. The heights of girls and boys in Year 12 were measured in centimetres. The results are listed below. Girls: 152, 162, 167, 170, 180, 193, 174, 157, 163, 172, 169, 174, 167, 160, 170, 171, 167, 174 Boys: 169, 180, 185, 179, 174, 185, 195, 181, 163, 176, 174, 174, 179, 183, 188, 188, 192, 192 a Represent this data in a back-to-back stem-and-leaf plot. b Describe the shape of the data for: i girls ii boys. c What comparisons can be made between the heights of boys and girls from the data?

Two-Way Tables Two-way tables are used to compare two groups of categorical data. They are useful in making comparisons between categories. e.g. A survey was conducted to investigate how many students played computer games. a Find the missing values marked A, B, C and D. b What percentage of boys play games sometimes? c What percentage of the students who never play games are girls?