WE HAVE BEEN LOOKING AT: Univariate data: Collecting sets of data and analysing it to see the results Ungrouped data set: a list of individual results (3, 4, 4, 2, 6, 5, 8, 5) Grouped data set: data is put into intervals rather than as individual results (e.g. 0-10, 11-20) Analysing measures of central tendency: Mean (average) Median (middle score when they are in order) Mode (most common)

13B – MEASURES OF SPREAD RANGE AND INTERQUARTILE RANGE

CONSIDER THESE EXAMPLES A music store owner has stores in Caroline Springs and Geelong. The number of CDs sold each day over one week is recorded below. Caroline Springs: 60, 50, 55, 48, 40, 52 Geelong: 85, 50, 15, 30, 60, 90 What do you notice about these data sets? What are your observations? Let’s look at the measures of central tendency (mean, median and mode): Caroline Springs: Mean= 50, Median = 50, No mode Geelong: Mean= 50, Median = 50, No mode If all we look at are the measures of central tendency, we would say that these data sets are very similar However, we can see that the Caroline Springs data is more clustered together than the Geelong data which is more spread out Therefore, it is important to look at measures of spread as well as measures of central tendency

RANGE AND INTERQUARTILE RANGE Remember from earlier: mean, median and mode are known as ‘measures of central tendency’ and tell is about the middle/centre points of the data we are analysing Today we are looking at range and interquartile range, which are known as ‘measures of spread’ and tell us how spread out/spaced out the data is A couple of formulas to remember: Range: This tells us how far the data is spread out from top (highest) to bottom (lowest) Interquartile range: This tells us the middle 50% of the data. This is considered to be a more reliable analysis of the data than the range

WORKED EXAMPLE: RANGE Find the range of the given data set: 2.1, 3.5, 3.9, 4.0, 4.7, 4.8, 5.2 (it helps to make sure the data is in order first) X max (highest score) = 5.2 X min (lowest score) = 2.1 Range = Range = 3.1

FINDING THE INTERQUARTILE RANGE Steps to follow: 1.Put the data in order (lowest to highest is easiest) 2.Split the data in half, so you have an equal number of scores in each half Note: if you have an ODD number of scores which doesn’t divide in half evenly, leave the middle number (median) out 3.Find the median of each half of the data (count inwards until you find the middle number. If there are an odd number of scores, find the average of the middle two scores) The median of the bottom half of the data is known as Quartile 1 or the lower quartile (Q 1 or Q L ) The median of the top half of the data is known as Quartile 3 or the upper quartile (Q 3 or Q U ) 4.Obtain the interquartile range (IQR) by calculating the difference between the upper and lower quartiles: IQR = Q 3 − Q 1

WORKED EXAMPLE: INTERQUARTILE RANGE Calculate the interquartile range (IQR) of the following set of data: 3, 2, 8, 6, 1, 5, 3, 7, 6 1.Put the data in order: Split the data in half: (5 is the odd one out in the middle, so we leave it out) 3.Find the median of each half of the data: For , the median is between 2 and 3 (2 + 3) ÷ 2 = 2.5 Therefore Q 1 is 2.5 For , the median in between 6 and 7 (6 + 7) ÷ 2 = 6.5 Therefore Q 3 is Obtain the interquartile range (IQR): IQR = Q 3 − Q 1 IQR = 6.5 – 2.5 IQR = 4

QUESTIONS Exercise 13B page 442: Questions 1, 2, 6, 9, 10