7.3 Find Measures of Central Tendency and Dispersion

Vocabulary Statistics: numerical values used to summarize and compare sets of data Measure of central tendency: number used to represent the center or middle set of data Mean - the average Median – the middle number Mode – number that occurs most

Vocabulary Measure of Dispersion: statistic that tells you how spread out the values are Range – biggest - smallest Standard Deviation: “sigma”

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 Office A: Mean: x = 14 + 17 + + 32 9 … 9 198 = 22 = Median: 20 Mode: 24 9 Office B: Mean: x = 8 + 11 + + 23 … 9 = 144 = 16 Median: 18 Mode: 18

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 SOLUTION Mean: x = 10 4 + 8 + 12 + + 7 … 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. Explain what that means. SOLUTION = 18 Office A: Range = 32 – 14 Office B: Range = 23 – 8 = 15 Because the range for office A is greater, its waiting times are more spread out.

EXAMPLE 3 Standardized Test Practice (14 22)2 – + (17 22)2 – + + (32 22)2 ... – = 290 9 Office A: = 5.7 9 Office B: = (8 16)2 + (11 16)2 + + (23 16)2 – ... 9 = 182 9 4.5 ANSWER The correct answer is D.

GUIDED PRACTICE for Examples 2 and 3 Find the range and standard deviation of the data set. 4, 8, 12, 15, 3, 2, 6, 9, 8, 7 Range = 15 – 2 SOLUTION = 13 = 3.8 Standard deviation