12- 3 Measures of Central Tendency and Dispersion
Quick Review
m Ihe _______________mean of a data set equals r_ ______^ i_ total number of data values' sum of the data values -n__^
median is the m iddle value in the data set w h e n th e values
are arranged in order. Ih e mode is th e d ata item th a t occurs
the m ost times. I h e range o f a set o f d a ta is th e difference
betw een the greatest a n d least d ata values.Ex a m p l e
Ih e quality ratings of 9 m ovies showing at a m ovie theater
near you are 5.6 ,7 .9 ,7 .0 , 5.9, 7.8, 6.2, 6.4, 5.2, and 5.6.
What are the m ean, m edian, m ode, and range of the data?
mean:
5.6 + 7.9 + 7.0 + 5.9 + 7.8 + 6.2 + 6.4 + 5.2 + 5.6 „ „
--------------------------------------------- 9 ----------------------------------------------= 6'4
5.2 5.6 5.6 5.9 6.2 6.4 7.0 7.8 7.9 Order the data.
median: 6.2 6.2 is the middle value.
mode: 5.6 5.6 occurs most often.
range: 7.9 - 5.2 = 2.7 Find difference between
greatest and least values.Ex e r c i s e s
Find the m ean, m edian, m ode, and range o f each data set.- points scored by a football team : 23 31 26 27 25 28
23 23 25 29 29 29 25 22 30 - clips p er package: 12 12 13 12 12 12 12 12 12
13 12 11 12 12 12 12 12 - Cats A v e te rin a ria n exam in es 9 cats. I h e w eights
of th e cats are 13.4 lb, 13.1 lb, 10.4 lb, 6.8 lb, 11.4 lb,
10.8 lb, 13.4 lb, 11.3 lb, a n d 9.3 lb. Find th e m ean,
m edian, an d m ode of th e data. W hich m easure of
central ten d en c y b est describes th e data? - Basketball A basketball player scores 22,19, 25, and
17 points in four games. How m any points does the
basketball player n e e d to score in th e fifth gam e to
average 22 points scored p e r game?
12-4 B o x -a n d -W h is k e r Plots
Quick Review
A box-and-whisker plot organizes d ata values into four
groups using th e m inim um value, th e first quartile, the
m edian, th e third quartile, an d th e m axim um value.Ex a m p l e
What box-and-whisker plot represents the test
scores below?
62 57 78 69 85 43 94 82 61 90 83 51 67 88 55
Arrange the data in o rder from least to greatest.43 51 55 57 61 62 67 69 78 82 83 85 88 90 94t t
minimum
—Qi m edian (Q2) Qb maximum
+ H h
40 50 60 70 80 90 100
IEx e r c i se s
Make a box-and-whisker plot o f each data set.- movie lengths (min):
125 117 174 131 142 108 188 162 155 167 129
133 147 175 150 - dog weights (lb):
23 15 88 34 33 49 52 67 42 71 28 - book lengths (pages):
178 223 198 376 284 156 245 202 315 266 - W hich box-and-w hisker plot represents th e data set
w ith th e greater interquartile range? Explain.
o 50
100 150
0
50 100 150788 Chapter 12 Chapter Review