Lesson 2

Hanze University of Applied Science GroningenNing Ding, PhDLecturer of International BusinessSchool (IBS)n.ding@pl.hanze.nl

What we are going to learn? • Review • Chapter 3-A: Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

ReviewReview A. Nominal B. Ordinal C. Interval D. RatioChapter 3-A:Central Tendency A. Ungrouped Data What is the level of measurement for these items related to a. Mean the newspaper business? b. Mode c. Median a. The number of papers sold each Sunday during 2006. B. Grouped Data a. Mean b. The departments, such as editorial, advertising , sports, etc. b. Mode c. Median c. A summary of the number of papers sold by county. d. The number of years with the paper for each employee. P14. N.2 Ch.1

ReviewReview A. Sample B. PopulationChapter 3-A:Central Tendency For the follow questions, would you collect information using a sample or a population? A. Ungrouped Data a. Mean b. Mode a. Statistics 201 is a course taught at a university. Professor A has c. Median taught nearly 1,500 students in the course over the past 5 years. You would like to know the average grade for the course B. Grouped Data a. Mean b. Mode c. Median b. You are looking forward to graduation project and your first job as a salesperson for one of five large corporations. Planning for your interviews, you will need to know about each company’s mission, profitability, products, and markets. P16. N.8 Ch.1

ReviewReviewChapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

ReviewReviewChapter 3-A:Central Tendency A. Ungrouped Data a. Mean A b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median A (21, 30) Around _______of the vehicles were seld below $21,000. a. 30% b. 43% c. 35 d. 43

Review A set of data contains 53 observations. The lowest value is 43 and the largest isReview 129. The data are to be organized into a frequency distribution. a. How many classes would you suggest?Chapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode 25 4 32, 265= 64, suggests 6 classes a. = b. c. 6 d. 7 c. Median B. Grouped Data b. What would you suggest as class interval & the lower limit of a. Mean the first class? b. Mode c. Median a. 10 130 - 4318 b. 15 c. d. 20 i> ≈ 15 6 Use interval of 15 And start first class at 40 P34. N.10 Ch.2

Central Tendency Parameter:Review a numerical characteristic of aChapter 3-A: population.Central Tendency Example: The fraction of U. S. voters who A. Ungrouped Data support Sen. McCain for President is a a. Mean b. Mode parameter. c. Median B. Grouped Data Statistic: a. Mean A statistic is a numerical characteristic of a sample. b. Mode c. Median Example: If we select a simple random sample of n = 1067 voters from the population of all U. S. voters, the fraction of people in the sample who support Sen. McCain is a statistic.

Central Tendency Parameter & StatisticsReviewChapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

Central Tendency: Mean Sum of all the values in the populationReview Population mean = Number of values in the populationChapter 3-A:Central Tendency μ= ∑X A. Ungrouped Data Example: N a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

Central Tendency: Mean Example:Review A sample of five executives received the following bonus last yearChapter 3-A: ($000):Central Tendency 14.0, 15.0, 17.0, 16.0, 15.0 ΣX 14.0+ ... +15.0 77 A. Ungrouped Data a. Mean b. Mode X= = = = 15.4 c. Median n 5 5 B. Grouped Data a. Mean b. Mode 1. Every set of interval- or ratio-level data has a mean c. Median 2. All the values are included in computing the mean 3. The mean is unique.

Central Tendency: Mean Example:Review Consider the set of values: 3, 8, and 4. The mean is 5.Chapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean Σ(X - X) = (3 - 5) + (8 - 5) + (4 - 5) = 0 b. Mode c. Median 4. The sum of the deviations of each value from the mean is zero.

Central Tendency: MeanReview Weighted Mean:Chapter 3-A: a set of numbers X1, X2, ..., Xn, with corresponding weightsCentral Tendency w1, w2, ...,wn, is computed from the following formula: A. Ungrouped Data a. Mean b. Mode c. Median (w 1 X1 + w 2 X 2 + ... + w n X n ) B. Grouped Data Xw = a. Mean b. Mode (w 1 + w 2 + ...w n ) c. Median

Central Tendency: Mean Weighted Mean:Review Example:Chapter 3-A: During a one hour period on a hot SaturdayCentral Tendency afternoon, Julie served fifty lemon drinks. She sold five drinks for $0.50, fifteen for A. Ungrouped Data a. Mean $0.75, fifteen for $0.90, and fifteen for $1.10. b. Mode Compute the weighted mean of the price of c. Median the drinks. B. Grouped Data a. Mean b. Mode c. Median 5($0.50)+15($0.75)+15($0.90)+15($1.10) Xw = 5 +15 +15 +15 $44.50 = = $0.89 50

Exercise (w 1 X 1 + w 2 X 2 + ... + w n X n ) Xw =Review (w 1 + w 2 + ...w n )Chapter 3-A: The Bookstall sold books via internet. Paperbacks are $1.00Central Tendency each, and hardcover books are $3.50. Of the 50 books sold on A. Ungrouped Data last Tuesday, 40 were paperback and the rest were hardcover. a. Mean What was the weighted mean price of a book? b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median (40 * $1.00+10 * $3.50) Xw = $1.50 50 a. $1.50 b. $1.54 c.$1.60 d.$1.64 P62. N.14 Ch.3

Central Tendency: Mode Mode:Review There is one situation in which the mode is the onlyChapter 3-A: measure of central tendency that can be used – whenCentral Tendency we have categorical, or non-numeric data. In this situation, we cannot calculate a mean or a median. The A. Ungrouped Data a. Mean mode is the most typical value of the categorical data. b. Mode c. Median B. Grouped Data Example: a. Mean Suppose I have collected data on religious affiliation of citizens of b. Mode the U.S. The modal, or most Typical value, is Roman c. Median Catholic, since The Roman Catholic Church is the largest religious organization in the U.S.

Central Tendency: Mode Mode:Review The value of the observation that appears most frequently.Chapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

Central Tendency: Mode Mode:Review The value of the observation that appears mostChapter 3-A: frequently.Central Tendency Example: A. Ungrouped Data a. Mean The exam scores for ten students are: b. Mode c. Median 81, 93, 84, 75, 68, 87, 81, 75, 81, 87. B. Grouped Data a. Mean b. Mode c. Median Because the score of 81 occurs the most often, it is the mode.

Central Tendency: Median Median:Review the midpoint of the values after they have been orderedChapter 3-A: from the smallest to the largest.Central Tendency A. Ungrouped Data a. Mean Example: b. Mode The ages for a sample of five college students are: c. Median 21, 25, 19, 20, 22 B. Grouped Data a. Mean b. Mode Arranging the data in ascending order gives: c. Median 19, 20, 21, 22, 25. Thus the median is 21.

Central Tendency: MedianReview For an even set of values, the median will be theChapter 3-A:Central Tendency arithmetic average of the two middle numbers. A. Ungrouped Data a. Mean b. Mode Example: c. Median The heights of four basketball players, in inches, are: B. Grouped Data a. Mean 76, 73, 80, 75 b. Mode c. Median Arranging the data in ascending order gives: 73, 75, 76, 80. Thus the median is 75.5

Central Tendency: Median Example: 72 68 65 70 75 79 73Review Finding the medianChapter 3-A:Central Tendency 65 68 70 72 73 75 79 A. Ungrouped Data a. Mean b. Mode c. Median 65 68 70 72 73 75 79 79 B. Grouped Data a. Mean 72.5 b. Mode c. Median 65 68 70 72 73 75 79 79,000 72.5 Median is not influenced by the extreme value.

ExerciseReview List below are the total automobile sales (in millionsChapter 3-A: of dollars) for the last 7 years. What was the medianCentral Tendency number of automobiles sold? What is the mode? A. Ungrouped Data 41 15 39 54 31 15 33 a. Mean b. Mode c. Median B. Grouped Data Mean= 32.57; Median=33; Mode=15 a. Mean b. Mode c. Median P65. N.22 Ch.3

ExerciseReviewChapter 3-A:Central Tendency A. Ungrouped Data a. Mean Mean Mode Median b. ModeCity c. Median - - - B. Grouped DataWind a. Mean - Southwest - b. Modedirection c. MedianTemperature 91 o F 92 o F 92 o FPavement - Wet & Dry Trace

amplehe Arithmetic Mean of Grouped Data -xample Central Tendency: Meancall in Chapter 2, weconstructed a frequency Recall in Chapter 2, we Reviewdistribution forfrequency the vehicle constructed aselling prices. The Chapter 3-A: distribution for the vehicle Central Tendencyinformation is repeated selling prices. The information is repeatedbelow. Determine the A. Ungrouped Data a. Mean below. Determine thearithmetic mean vehicle b. Mode arithmetic mean vehicle c. Medianselling price. selling price. B. Grouped Data a. Mean b. Mode c. Median 33

he Arithmetic Mean of Grouped Data Central Tendency: Mean Review Chapter 3-A: Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

Central Tendency: MeanReviewChapter 3-A:Central Tendency Determine the mean of the following frequency distribution. A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median a. 15.00 b. 12.54 c.11.54 d.12.67 X=380/30=12.67 P87. N.58 Ch.3

Central Tendency: Mode , we Review Example: Finding the mode for grouped dataequency Step 1: Chapter 3-A: Step 2:he vehicleModal class with the highest frequency Midpoint of the modal class Central Tendency is the mode heA. Ungrouped Data a. Mean peated b. Mode c. Medianne the B. Grouped Data vehicle a. Mean b. Mode 19.5 c. Median

Central Tendency: Mode Example: Finding the mode for grouped dataReviewChapter 3-A: Step 1:Central Tendency Modal class with the highest frequency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

Central Tendency: Mode Step 2:Review Midpoint of the modal class is the modeChapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median

Central Tendency: Median Step 3:ReviewChapter 3-A: Draw two lines (value & position)Central Tendency A. Ungrouped Data Value: 100 A Median 150 a. Mean b. Mode Position: 201 300.5 B 388 c. Median B. Grouped Data a. Mean Median – 100 300.5 – 201 b. Mode = c. Median 150 - 100 388 - 201 300.5 – 201 Median = * 50 + 100 = 126.60 (dollars) 388 - 201

Exercise SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. Describe the central tendency:ReviewChapter 3-A:Central Tendency A. Ungrouped Data a. Mean b. Mode c. Median B. Grouped Data a. Mean b. Mode c. Median Mode = 45 (years) X= a. 20.00 a. 30.50 2410 / 60c.45.00 d.45.50 e. 50.00 b. 40.00 b. 38.00 = 40.17 (years) c.38.25 d.40.25 e. 41.25 f.50.50 f.42.25 a. 40.17 b. 200.83 c.482.00 d.120.50 e. 48.20 Median = ? (years) P87 N.60 Ch.3

Exercise a. 30.00 b. 38.00 c.38.25 d.40.25 e. 41.25 f.42.25Step 1: Define the location of the median Step 2: Calculate the median M Lm=(60+1)/2=30.5 Value:40 50 Location: 28 48 30.5 30.5-28 M-40 = 48-28 50-40 Median= 41.25 years P87 N.60 Ch.3

What we have learnt? • ReviewReviewChapter 3-A:Central Tendency • Chapter 3-A: Central Tendency A. Ungrouped A. Ungrouped Data Data a. Mean a. Mean b. Mode c. Median b. Mode B. Grouped Data c. Median a. Mean b. Mode B. Grouped Data c. Median a. Mean b. Mode c. Median

Lesson 2

by Ning Ding on Jun 29, 2012

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