Prerequisite Skills VOCABULARY CHECK Copy and complete the statement. 1. The probability of an event is a number from ? to ? that indicates the likelihood the event will occur. 2. The binomial distribution at the right is not skewed. Instead, it is ?. ANSWER 0, 1 ANSWER normal

Prerequisite Skills SKILL CHECK You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the event. 5. An odd number is chosen. 6. A perfect square is chosen. 8. A factor of 50 is chosen. 7. A multiple of 3 is chosen. ANSWER

{ 11.1 Find Measures of Central Tendency and Dispersion

EXAMPLE 1 Find measures of central tendency Waiting Times The data sets at the right give the waiting times (in minutes) of several people at two veterinary offices. Find the mean, median, and mode of each data set. SOLUTION Median: 20 Mode: = 22 = Office A : Mean: x = …

EXAMPLE 1 Find measures of central tendency = 16 Median: 18 Mode: 18 9 Office B : Mean: x = … 9 = 144

GUIDED PRACTICE for Example 1 TRANSPORTATION 1. The data set below gives the waiting times (in minutes) of 10 students waiting for a bus. Find the mean, median, and mode of the data set. 4, 8, 12, 15, 3, 2, 6, 9, 8, 7 Mean: x = … SOLUTION 10 = 74 = 7.4 Median: 7.5 Mode: 8

{ EXAMPLE 2 Find ranges of data sets Find the range of the waiting times in each data set in Example 1. SOLUTION Office A: Range = 32 – 14 Office B: Range = 23 – 8 Because the range for office A is greater, its waiting times are more spread out. = 18 = 15

{ EXAMPLE 3 Standardized Test Practice SOLUTION Office B: = (8 16) 2 + (11 16) (23 16) 2 – – –... 9 = = Office A : = (14 22) 2 – + (17 22) (32 22) 2... – – ANSWER The correct answer is D.

{ GUIDED PRACTICE for Examples 2 and 3 2. Find the range and standard deviation of the data set in Guided Practice Exercise 1 on page 745. Range = 15 – 2 SOLUTION = 13 = (2 – 7.4) 2 + (4 – 7.4) (15 – 7.4) 2... = = 3.8 Standard deviation = (x 1 – x) 2 + (x 2 – x) 2 n + + (x n – x) 2...

{ EXAMPLE 4 Examine the effect of an outlier You are competing in an air hockey tournament. The winning scores for the first 10 games are given below. 14, 15, 15, 17, 11, 15, 13, 12, 15, 13 a. Find the mean, median, mode, range,and standard deviation of the data set. Air Hockey b. The winning score in the next game is an outlier, 3. Find the new mean, median, mode, range, and standard deviation.

{ EXAMPLE 4 Examine the effect of an outlier c. Which measure of central tendency does the outlier affect the most? the least? d. What effect does the outlier have on the range and standard deviation? SOLUTION a. Mean: = x = 14 Median: 14.5 Mode: 15 Range: 17 – 11 = 6

{ EXAMPLE 4 Examine the effect of an outlier = = x b. Mean: Median: 14 Mode: 15 Range: 17 – Std. Dev.: = (14 14) 2 + (15 14) (13 14) 2 – – – 10 … 3.5 (14 13) 2 + (15 13) ( 3 13) 2 – – – Std. Dev.: = 11 … = 14

{ EXAMPLE 4 Examine the effect of an outlier c. The mean is most affected by the outlier. The mode is least affected by the outlier. d. The outlier causes both the range and standard deviation to increase.

{ GUIDED PRACTICE for Example 4 3. What If? In part (b) of Example 4, suppose the winning score in the next game is 25 instead of 3. Find the new mean, median, mode, range, and standard deviation of the data set. SOLUTION Mean: = x = 15 Median: 15 Mode: 15 Range: 25 – 11 (14 15) 2 + (15 15) ( 25 15) 2 – – – Std. Dev.: = 11 … = 3.5 = 14

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