7The dot plot on the right shows the shoe sizes of a sample of Year 11 students.aFor this data, find:ithe meaniithe medianiiithe mode.bIf the outlier is removed, state what will happen to:789101112Shoe size

cA shoe store needs to buy more shoes for a back-to-school sale. Which measure of location is the most appropriate for the store to use in this situation?8The numbers of accidents per month in a motor vehicle factory over a year were:300121600210aFor this data, find:

bIf the workplace union representatives wanted to complain about the lack of safety at the factory, which statistic would they choose?

If the factory managers wanted to claim that there were very few accidents at the factory, which statistic would they choose?

A safety researcher chose the median as the average. Why did he do this?9The heights, in centimetres, of a team of basketball players are:204 195 184 189 193 178 aFor this data, find:ithe mean, correct to one decimal place iithe median.bThe 184 cm player is replaced by a 200 cm player. Describe how this will affect:199

10The stem-and-leaf plot on the right shows the maximum daily temperatures (in °C) in Port Macquarie for the last two weeks in December.Source: Bureau of MeteorologyaFor this data, find: Leaf232 4 4 5 6 6 7 7 1

bWhich measure of location is the most appropriate for describing the average maximum daily temperature?6789101112Shoe sizeStemLeaf232 4 4 5 6 6 7 7 1 7 8 8 94

9.Analysing data4059-04 Quartiles, deciles and percentilesThe median and quartilesSUMMARYThe three quartilesof a data set are those values that separate the data into quarters.•Thelower quartile, Q1or QL, separates the bottom quarter (25%) of scores from the rest of the scores.•Theupper quartile, Q3or QU, separates the top quarter (25%) of scores from the rest of the scores.•Themiddle quartile, Q2, is the median, and separates the two middle quarters.SUMMARYTo find the quartiles of a data set:Step 1:sort the scores in order, find the median and call it Q2Step 2:find the median of the bottom half of scores and call it Q1Step 3:find the median of the top half of scores and call it Q3.These speeds (in km/h) were recorded for 11 cars driving along a major country road:10710486951008112084789392When we sort the scores, in ascending order, we can find the quartiles:78 81 84Q1=84Q2=93Q3=10486 929395 100 104 107 120A speed of 107 km/h is in the top quarter of scores.A speed of 81 km/h is in the bottom quarter of scores.A speed of 100 km/h is in the 2nd top quarter of scores.EXAMPLE 10Find the quartiles for each data set below.aThe marks obtained by a class of students for an art project.51 41 60 38 46 57 39 61 43 64