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1-2 Chapter 22 Business Statistics McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.

1-3 Define and calculate the mean Explain and calculate a weighted mean Define and calculate the median Define and identify the mode Business Statistics #22 Learning Unit Objectives Mean, Median, and Mode LU22.1

1-4 Mean - Average used to indicate a single value that represents an entire group of numbers Median - A measurement that indicates the center of the data (Average) Terminology Mode - a measurement that records values. The value that occurs most often

1-5 Mean Mean = Sum of all values Number of values What is the mean of the following daily sales? MonTuesWed.Thur.Fri.Sat. $200$325$570$711$880$950 Mean = $200 + $325 + $570 + $711 + $880 +$950 = $606 6

1-6 Weighted Mean Weighted Mean = Sum of products Sum of frequencies What is the weighted mean (GPA) for the student? Credit Grade Points Courses attempted received (Credits x Grade) Business Math3 B 9 (3 x 3) Speech3 C 6 (3 x 2) Accounting4 A 16 (4 x 4) English3 B 9 (3 x 3) =

1-7 Finding the Median of a Group of Values Step 1. Orderly arrange values from the smallest to the largest Step 2. Find the middle value a. Odd number of values: Median is the middle value. Divide the total number of numbers by 2. The next-higher number is the median. B. Even number of values: Median is the average of the two middle values. Find the median age 42, 35, 87, 23, 50 23, 35, 42, 50, 87 35, 42, 50, Find the median age 42, 35, 87, 50

1-8 Mode 6, 8, 0, 3, 4, 23, 57, 31, 22, 47, 31, 2, 6, 9, is the mode since it is listed 3 times The value that occurs most often If two or more numbers appear most often, you may have two or more modes. If all the values are different, there is no mode

1-9 Find Mean, Median, Mode Here are the monthly rainfall totals for the past year: 2.4; 1.9; 3.7; 4.2; 3.4; 2.7; 1.7; 1.9;.8; 2.1;.7; 2.3 Calculate the monthly Mean: 30.2 / 12 = 2.52 Find the Median: What is the Mode: 1.9

1-10 Prepare a frequency distribution Prepare bar, line, and circle graphs Calculate price relatives and cost comparisons Business Statistics #22 Learning Unit Objectives Frequency Distributions and Graphs LU22.2

1-11 Frequency Distribution A way of collecting and organizing raw data The average amount of alcoholic beverages consumed per week Drinks Tally Frequency 0 l1 1 l ll2 4 ll2 5 lll3 6 l1 7 l1 8 ll2 9 l1 10 l1 11 l1 Frequency distribution table

1-12 Bar Graph Frequency of consumption Number of drinks

1-13 Line Graph Average cost of College tuition Year

1-14 Circle Graph 12.9% 56.9% 17.3% Revenues 1st Qtr $20,400 2nd Qtr $27,400 3rd Qtr $90,000 4th Qtr $20,400

1-15 INDEX NUMBERS Use to compare when values (prices) change over time May be used to compare geographically diverse values Commonly associated with the CPI (consumer price index) Express relative changes over time in relation to a base Public Data Query

1-16 Index Numbers Price relative = Current price x 100 Base year’s price A computer cost $850 today relative to a cost of $1,300 some 5 years ago. What is the relative price? $850 x 100 = = 65.4 $1,300

1-17 Explain and calculate the range Define and calculate the standard deviation Estimate percentage of data by using standard deviations Business Statistics #22 Learning Unit Objectives Measures of Dispersion (Optional Section) LU22.3

1-18 Step 1. Find the mean of the set of data Step 2. Subtract the mean from each piece of data to find each deviation Step 3. Square each deviation (multiply the deviation by itself) Step 4. Sum all squared deviations Step 5. Divide the sum of the squared deviations by n - 1, where n equals the number of pieces of data Step 6. Find the square root ( ) of the number obtained in Step 5. This is the standard deviation Intended to measure the spread of data around the mean Standard Deviation

1-19 Step 1 ( ) = 6 5 Step 2Step 3 DataData-Mean(Data-Mean) = = = = = 636 Total 094 (Step 4) Step 5: Divide by n-1: 94 = 94 = Step 6: The square root of 23.5 is 4.8 Data set x x x x x Standard Deviation