Copyright © 2009 Pearson Education, Inc. Chapter 13 Section 5 - Slide 1 Section 5 Measures of Central Tendency

Chapter 13 Section 5 - Slide 2 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN How to determine: Mode Median Mean Midrange

Chapter 13 Section 5 - Slide 3 Copyright © 2009 Pearson Education, Inc. Definitions An average is a number that is representative of a group of data. The arithmetic mean, or simply the mean, is symbolized by, when it is a sample of a population or by the Greek letter mu, , when it is the entire population.

Chapter 13 Section 5 - Slide 4 Copyright © 2009 Pearson Education, Inc. Mean The mean,, is the sum of the data divided by the number of pieces of data. The formula for calculating the mean is where represents the sum of all the data and n represents the number of pieces of data.

Chapter 13 Section 5 - Slide 5 Copyright © 2009 Pearson Education, Inc. Example-find the mean Find the mean amount of money parents spent on new school supplies and clothes if 5 parents randomly surveyed replied as follows: $327 $465 $672 $150 $230

Chapter 13 Section 5 - Slide 6 Copyright © 2009 Pearson Education, Inc. Median The median is the value in the middle of a set of ranked data. Example: Determine the median of $327 $465 $672 $150 $230. Rank the data from smallest to largest. $150 $230 $327 $465 $672 middle value (median)

Chapter 13 Section 5 - Slide 7 Copyright © 2009 Pearson Education, Inc. Example: Median (even data) Determine the median of the following set of data: 8, 15, 9, 3, 4, 7, 11, 12, 6, 4. Rank the data: There are 10 pieces of data so the median will lie halfway between the two middle pieces (the 7 and 8). The median is (7 + 8)/2 = Median = 7.5

Chapter 13 Section 5 - Slide 8 Copyright © 2009 Pearson Education, Inc. Mode The mode is the piece of data that occurs most frequently. Example: Determine the mode of the data set: 3, 4, 4, 6, 7, 8, 9, 11, 12, 15. The mode is 4 since it occurs twice and the other values only occur once.

Chapter 13 Section 5 - Slide 9 Copyright © 2009 Pearson Education, Inc. Midrange The midrange is the value halfway between the lowest (L) and highest (H) values in a set of data. Example: Find the midrange of the data set $327, $465, $672, $150, $230.

Chapter 13 Section 5 - Slide 10 Copyright © 2009 Pearson Education, Inc. Example The weights of eight Labrador retrievers rounded to the nearest pound are 85, 92, 88, 75, 94, 88, 84, and 101. Determine the a) mean b) median c) mode d) midrange e) rank the measures of central tendency from lowest to highest.

Chapter 13 Section 5 - Slide 11 Copyright © 2009 Pearson Education, Inc. Example--dog weights 85, 92, 88, 75, 94, 88, 84, 101 (continued) a. Mean b. Median-rank the data 75, 84, 85, 88, 88, 92, 94, 101 The median is 88.

Chapter 13 Section 5 - Slide 12 Copyright © 2009 Pearson Education, Inc. Example--dog weights 85, 92, 88, 75, 94, 88, 84, 101 c. Mode-the number that occurs most frequently. The mode is 88. d. Midrange = (L + H)/2 = ( )/2 = 88 e. Rank the measures, lowest to highest 88, 88, 88,

Chapter 13 Section 5 - Slide 13 Copyright © 2009 Pearson Education, Inc. Measures of Position Measures of position are often used to make comparisons. Two measures of position are percentiles and quartiles.

Chapter 13 Section 5 - Slide 14 Copyright © 2009 Pearson Education, Inc. To Find the Quartiles of a Set of Data 1.Order the data from smallest to largest. 2.Find the median, or 2 nd quartile, of the set of data. If there are an odd number of pieces of data, the median is the middle value. If there are an even number of pieces of data, the median will be halfway between the two middle pieces of data.

Chapter 13 Section 5 - Slide 15 Copyright © 2009 Pearson Education, Inc. To Find the Quartiles of a Set of Data (continued) 3.The first quartile, Q 1, is the median of the lower half of the data; that is, Q 1, is the median of the data less than Q 2. 4.The third quartile, Q 3, is the median of the upper half of the data; that is, Q 3 is the median of the data greater than Q 2.

Chapter 13 Section 5 - Slide 16 Copyright © 2009 Pearson Education, Inc. Example: Quartiles The weekly grocery bills for 23 families are as follows. Determine Q 1, Q 2, and Q

Chapter 13 Section 5 - Slide 17 Copyright © 2009 Pearson Education, Inc. Example: Quartiles (continued) Order the data: Q 2 is the median of the entire data set which is 190. Q 1 is the median of the numbers from 50 to 172 which is 95. Q 3 is the median of the numbers from 210 to 330 which is 270.

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the mean. a.13 b.14 c.15 d.16

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the mean. a.13 b.14 c.15 d.16

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the mode. a.13 b.14 c.15 d.16

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the mode. a.13 b.14 c.15 d.16

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the median. a.13 b.14 c.15 d.16

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the median. a.13 b.14 c.15 d.16

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the midrange. a.31 b.15.5 c.10 d.7

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the midrange. a.31 b.15.5 c.10 d.7

Slide Copyright © 2009 Pearson Education, Inc. For the set of data 12, 13, 15, 15, 16, 19 determine the midrange. a. b. c. d.