Chapter 22 Statistics

Learning Unit Objectives #22 Business Statistics Learning Unit Objectives LU22.1 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

Learning Unit Objectives #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

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

Terminology Median - A measurement that indicates the center of the data (Average) 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

Mean Mean = Sum of all values Number of values What is the mean of the following daily sales? Sun. Mon. Tues. Wed. Thur. Fri. Sat. $400 $100 $68 $115 $120 $68 $180 Mean = $400 + $100 + $68 + $115 + $120 +$68 + $180 = $150.14 7

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) Intro to Comp 4 A 16 (4 x 4) Psychology 3 B 9 (3 x 3) English Comp. 3 B 9 (3 x 3) Business Law 3 C 6 (2 x 3) Business Math 3 B 9 (3 x 3) 16 49 49 = 3.1 16

Finding the Median of a Group of Values Step 1. Orderly arrange values from the smallest to the largest Find the median age 42, 35, 87, 23, 50 Step 2. Find the middle value Odd number of values: Median is the middle value. Divide the total number of numbers by 2. (5/2 = 2 ½). The next-higher number is the median. B. Even number of values: Median is the average of the two middle values. 23, 35, 42, 50, 87 Find the median age 42, 35, 87, 50 35, 42, 50, 87 42 + 50 2 46

3 is the mode since it is listed 4 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 3 is the mode since it is listed 4 times 3, 4, 5, 6, 3, 8, 9, 3, 5, 3

Frequency Distribution A way of collecting and organizing raw data Price of Tally Frequency Computer $1,000 llll 5 2,000 l 1 3,000 llll 5 4,000 l 1 5,000 ll 2 6,000 ll 2 7,000 l 1 8,000 l 1 9,000 l 1 10,000 l 1 Computer costs 1000 7000 4000 5000 3000 2000 8000 9000 6000 10000 Frequency distribution table

Bar Graph Frequency of purchase Price of Computers 2000 4000 6000 8000 10000 Price of Computers

Bar Graph Class Frequency $1000 - $ 3,000.99 11 $3001 - 5,000.99 3 $1000 - $ 3,000.99 11 $3001 - 5,000.99 3 $5001 - 7,000.99 3 $8001 - 9,000.99 2 $9001 - 11,000.99 1 Frequency of purchase $3,001- $5,000.99 $7,001- $9,000.99

Average cost of College Line Graph Average cost of College tuition Year

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

Find the range of the following values: 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

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 = 65.38 = 65.4 $1,300

Consumer Price Index (in percent) Expense Atlanta Chicago NY LA Food 131.9 130.3 139.6 130.9 Housing 128.8 131.4 139.3 139.3 Clothing 133.8 124.3 121.8 126.4 Medical care 177.6 163.0 172.4 163.3

Intended to measure the spread of data around the mean 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

Standard Deviation Data Set A x x x x x Step 1 (1 + 2 + 5 + 10 + 12) = 6 (Mean) 5 Step 2 Step 3 Data Data-Mean (Data-Mean) 1 1- 6 = -5 25 2 2 - 6 = -4 16 5 5 - 6 = -1 1 10 10 - 6 = 4 16 12 12 - 6 = 6 36 Total 0 94 (Step 4) Step 5: Divide by n-1: 94 = 94 = 23.5 5-1 4 Step 6: The square root of 23.5 is 4.8 Data Set A 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

Standard Deviation Data Set B x x x x x Step 1 (4 + 4 + 5 + 8 + 9) = 6 (Mean) 5 Step 2 Step 3 Data Data-Mean (Data-Mean) 1 4- 6 = -2 4 2 4 - 6 = -2 4 5 5 - 6 = -1 1 10 8 - 6 = 2 4 12 9 - 6 = 3 9 Total 0 22 (Step 4) Step 5: Divide by n-1: 22 = 22 = 5.5 5-1 4 Step 6: The square root of 5.5 is 2.3 Data Set B 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 2.3

Problem 22-19 .35 x 360 = 126 .28 x 360 = 100.8 .20 x 360 = 72 .17 x 360 = 61.2 Misc. 17% Transportation 35% Food and entertainment 20% Hotel 28%

Problem 22-20 Frequency $0- $5.99 5 5 $6- $11.99 3 3 $12- $17.99 4 4 Intervals Tally Frequency $0- $5.99 5 5 $6- $11.99 3 3 $12- $17.99 4 4 $18- $23.99 2 2

Problem 22-21 Tally Day Bagels Product 150 9 9 x 150 = 1,350 7, 510 7,510/ 30 = 250.33= 250 Bagels

Problem 22-22 Thousands of dollars