page 263 #1ab, 2, 5, 7, 10b, 13, 16

Times Midpoint, mi Frequency, fi mifi cumulative freq4-5 4.5 32 144 325-6 5.5 50 275 826-7 6.5 125 812.5 2077-8 7.5 67 502.5 2748-9 8.5 108 918 382

Median:

13)

6.2February-19-152:39 PM

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Ch 6.2 - Measures of Spread

variability: how samples differ from each other; more similar samples mean lower variability, which is a better representation of the population

percentile: the percent of all the data that are less than or equal to a specific data value

The median is also called the 50th percentile. Why?50% of the data values are less than or equal to the median (and 50% are greater or equal)

Percentile Rank:

p is the percentile, n is the size of the population, R is the whole number rank of the data point (round down if necessary)

Percentile:

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p is percentile, L is the number of data less than the point, E is the number of data equal to the point, n is size of population

E.g. marks on our 5.1 quiz9, 10.5, 11.5, 10.5, 11.5, 10.5, 11, 12, 9.5, 7, 11, 9, 11.5, 11.5(out of 12)

1. Calculate the 80th percentile.

1. What percentile is a mark of 10.5?

2. What percentile is a mark of 9.5?

Homework: page 275 #1

p=25th percentile

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quartiles: three points that divide the data set into four equal groups

• first quartile (Q1) is the _______ percentile• second quartile (Q2) is the _________, the ________ percentile• third quartile (Q3) is the ________ percentile

interquartile range: the difference between the first and third quartiles (IQR = Q3 - Q1)https://www.mathsisfun.com/data/quartiles.htmlNOTE: see page 269 for box and whisker plots

E.g.For the following data set, determine the median, range, first and third quartiles, and interquartile range

Golf Score Frequency Cumulative Frequency70–75 1 175–80 2 380–85 8 1185–90 4 1590–95 2 1795–100 5 22100–105 3 25

median

range

first quartile

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third quartile

IQR

outlier: a piece of data that is more than 1.5 times the IQR below Q1 or above Q3in the above example,

HW: page 275 #1, 3, 5, 9

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