Chapter 22 - Business statistics. After you have mastered the material in this chapter, you will be able to: Define and calculate the mean, explain and calculate a weighted mean, define and calculate the median, define and identify the mode, prepare a frequency distribution, prepare bar, line, and circle graphs, calculate price relatives and cost comparisons, explain and calculate the range, define and calculate the standard deviation, estimate percentage of data by using standard deviations.
Chapter 22 Business Statistics McGrawHill/Irwin ©2011 The McGrawHill Companies, All Rights Reserved #22 LU22.1 Business Statistics Learning Unit Objectives Mean, Median, and Mode Define and calculate the mean Explain and calculate a weighted mean Define and calculate the median Define and identify the mode 222 #22 Business Statistics Learning Unit Objectives LU22.2 Frequency Distributions and Graphs Prepare a frequency distribution Prepare bar, line, and circle graphs Calculate price relatives and cost comparisons 223 #22 Business Statistics Learning Unit Objectives LU22.3 Measures of Dispersion (Optional Section) Explain and calculate the range Define and calculate the standard deviation Estimate percentage of data by using standard deviations 224 Terminology Mean Average used to indicate a single value that represents an entire group of numbers Mode a measurement that records values. The value that occurs most often 225 Median A measurement that indicates the center of the data (Average) Mean Mean = Sum of all values Number of values The accountant of Bill’s Sport Shop told Bill, the owner, that the average daily sales for the week were $150.14. The accountant stressed that $150.14 was an average and did not represent specific daily sales. Bill wanted to know how the accountant arrived at $150.14 Sun. Mon Tues Wed Thur Fri Sat. $400 $180 $100 $68 $115 $120 $68 Mean = $400 + $100 + $68 + $115 + $120 +$68 + $180 = $150.14 226 Weighted Mean Weighted Mean = Sum of products Sum of frequencies How Jill Rivers calculated her GPA to the nearest tenth Credit Grade Points Courses attempted received (Credits x Grade) Intro to Comp A 16 (4 x 4) Psychology B 9 (3 x 3) English Comp B 9 (3 x 3) Business Law C 6 (2 x 3) Business Math B 9 (3 x 3) 16 49 227 49 = 3.1 16 Finding the Median of a Group of Values Look below at the following yearly salaries of the employees of Rusty’s Clothing Shop Alice Knight $95,000 Jane Wang Jane Hess $27,000 Bill Joy Joel Floyd $32,000 $67,000 $40,000 Find median value of all employees Find median value If Jane Hess ($27,000) were not on the payroll 228 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. (5/2 = 2 ½). The nexthigher number is the median B. Even number of values: Median is the average of the two middle values 229 Find the median value 95, 27, 32, 67, 40 27, 32, 40, 67, 95 Find the median value 95, 32, 67, 40 32, 40, 67, 95 40 + 67 2 53.5 Mode 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 3, 4, 5, 6, 3, 8, 9, 3, 5, 3 2210 3 is the mode since it is listed 4 times Frequency Distribution A way of collecting and organizing raw data Price of Tally Frequency Computer $1,000 llll 2,000 l 3,000 llll 1000 7000 4000 1000 5000 1000 3000 4,000 l 5,000 ll 5000 2000 3000 3000 3000 8000 9000 6,000 ll 7,000 l 8,000 l 3000 6000 6000 1000 10000 1000 9,000 l 10,000 l Computer costs 2211 5 2 1 1 Frequency distribution table Bar Graph Frequency of purchase 4.5 3.5 2.5 1.5 0.5 2212 1000 2000 3000 5000 4000 6000 7000 8000 Price of Computers 9000 10000 Bar Graph Frequency $1000 $ 3,000.99 $3001 5,000.99 $5001 7,000.99 $8001 9,000.99 $9001 11,000.99 2213 11 3 3 2 1 Frequency of purchase Class 15 10 $1,000 $5,001 $9,001 $3,000.99 $7,000.99 $11,000.99 $3,001 $7,001 $5,000.99 $9,000.99 Circle Graph 12.9% 12.9% 17.3% 56.9% 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Revenues 1st Qtr. $20,400 2nd Qtr $27,400 3rd Qtr $90,000 4th Qtr $20,400 2214 Measure of Dispersion • Measure of Dispersion – a number that describes how the numbers of a set of data are spread out or dispersed • Range – The difference between the two extreme values (highest and lowest) in a group of values or a set of data Range = Highest value – Lowest value Find the range of the following values: 83.6, 77.3, 69.2, 93.1, 85.4, 71.6 Range = 93.1 – 69.2 = 23.9 2215 Index Numbers Price relative = Current price x 100 Base year’s price A calculator may cost $9 today relative to a cost of $75 some 30 years ago. What is the relative price? $9 x 100 = .12 = 12% $75 2216 Consumer Price Index (in percent) Table 22.1 Expense Atlanta Chicago NY LA Food Housing Clothing Medical care 2217 131.9 128.8 133.8 177.6 130.3 131.4 124.3 163.0 139.6 139.3 121.8 172.4 130.9 139.3 126.4 163.3 Standard Deviation Intended to measure the spread of data around the mean Step 6. Find the square root ( ) of the number obtained in Step 5. This is the standard deviation Step 5. Divide the sum of the squared deviations by n 1, where n equals the number of pieces of data Step 4. Sum all squared deviations Step 3. Square each deviation (multiply the deviation by itself) Step 2. Subtract the mean from each piece of data to find each deviation Step 1. Find the mean of the set of data 2218 Standard Deviation Step 1 (1 + 2 + 5 + 10 + 12) = 6 (Mean) Data Set A Step 2 Step 3 Data DataMean (DataMean) 1 6 = 5 25 2 6 = 4 16 5 6 = 1 1 10 10 6 = 4 16 12 12 6 = 6 36 Total 0 94 (Step 4) x x x x x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 The standard deviation of data set A is 4.8 Step 5: Divide by n1: 94 = 94 = 23.5 51 4 Step 6: The square root of 23.5 is 4.8 2219 Standard Deviation Step 1 (4 + 4 + 5 + 8 + 9) = 6 (Mean) Data Set B x x x x x Step 2 Step 3 Data DataMean (DataMean) 4 6 = 2 4 4 6 = 2 4 5 6 = 1 1 8 6 = 2 4 9 6 = 3 9 Total 0 22 (Step 4) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 10 12 The standard deviation of data set A is 2.3 Step 5: Divide by n1: 22 = 22 = 5.5 51 4 Step 6: The square root of 5.5 is 2.3 2220 ... Explain and calculate a weighted mean Define and calculate the median Define and identify the mode 22 2 #22 Business Statistics Learning Unit Objectives LU22.2 Frequency Distributions and Graphs Prepare a frequency distribution... Prepare bar, line, and circle graphs Calculate price relatives and cost comparisons 22 3 #22 Business Statistics Learning Unit Objectives LU22.3 Measures of Dispersion (Optional Section) Explain and calculate the range... English Comp B 9 (3 x 3) Business Law C 6 (2 x 3) Business Math B 9 (3 x 3) 16 49 22 7 49 = 3.1 16 Finding the Median of a Group of Values