MEASURES OF CENTRAL TENDENCY AND MEASURES OF …

1 I. INTRODUCTION AND FOCUS QUESTIONSMEASURES OF CENTRAL TENDENCY AND MEASURES OF VARIABILITY443 Have you ever wondered why a certain size of shoe or brand of shirt is made more available than other sizes? Have you asked yourself why a certain basketball player gets more playing time than the rest of his team mates? Have you thought of comparing your academic performance with your classmates? Have you wondered what score you need for each subject area to qualify for honors? Have you, at a certain time, asked yourself how norms and standards are made?444 In this module you will find out the MEASURES of CENTRAL TENDENCY and MEASURES of vari-ability. Remember to search for the answer to the following question(s): How can I make use of the representations and descriptions of a given set of data? What is the best way to measure a given set of data?

2 In this module, you will examine these questions when you study the following LESSONS AND COVERAGE Lesson 1: MEASURES of CENTRAL TENDENCY of Ungrouped Data Lesson 2: MEASURES of Variability of Ungrouped Data Lesson 3: MEASURES of CENTRAL TENDENCY of Grouped Data Lesson 4: MEASURES of Variability of Grouped DataPurefoods TJ Giants | 2007-08 PBA Philippine Cup In these lessons, you will learn to:LessonObjectives:1 Find the mean, median , and mode of ungrouped data Describe and illustrate the mean, median , and mode of ungrouped data2 Discuss the meaning of variability Calculate the different MEASURES of variability of a given ungrouped data: range, standard deviation, and variance Describe and interpret data using MEASURES of CENTRAL TENDENCY and MEASURES of variability3 Find the mean, median , and mode of grouped data Describe and illustrate the mean, median , and mode of grouped data4 Discuss the meaning of variability Calculate the different MEASURES of variability of a given grouped data: range, standard deviation, and variance Describe and interpret data using MEASURES of CENTRAL TENDENCY and MEASURES of variabilityModule MapModule Map Here is a simple map of the lessons that will be covered in this module.

3 Descriptive StatisticsUngrouped DataMeasures of CENTRAL TendencyMeasures of CENTRAL TendencyMeasures of VariabilityMeasures of VariabilityGrouped Data To do well in this module, you will need to remember and do the following: 1. Study each part of the module carefully. 2. Take note of all the formulas given in each Have your own scientific calculator. Make sure you are familiar with the keys and functions in your PRE - ASSESSMENT Find out how much you already know about this topic. On a separate sheet, write only the letter of the choice that you think best answers the question. 1. Which measure of CENTRAL TENDENCY is generally used in determining the size of the most saleable shoes in a department store? a. mean c. mode b. median d. range2. The most reliable measure of variability is _____.

4 A. range c. average deviation b. variance d. standard deviation3. For the set of data consisting of 8, 8, 9, 10, 10, which statement is true? a. mean = mode c. mean = median b. median = mode d. mean < median4. Which measure of CENTRAL TENDENCY is greatly affected by extreme scores? a. mean c. mode b. median d. none of the three5. Margie has grades 86, 68 and 79 in her first three tests in Algebra. What grade must she obtain on the fourth test to get an average of 78? a. 76 c. 78 b. 77 d. 796. What is the median age of a group of employees whose ages are 36, 38, 18, 10 16 and 15 years? a. 10 c. 16 b. 15 d. 177. Nine people gave contributions in pesos 100, 200, 100, 300, 300, 200, 200, 150, 100, and 100 for a door prize.

5 What is the median contribution? a. Php 100 c. Php 175 b. Php 150 d. Php 2004478. If the heights in centimetres of a group of students are 180, 180, 173, 170, and 167, what is the mean height of these students? a. 170 c. 174 b. 173 d. 1809. If the range of a set of scores is 14 and the lowest score is 7, what is the highest score? a. 21 c. 14 b. 24 d. 710. What is the standard deviation of the scores 5, 4, 3, 6 and 2? a. 2 b. c. 3 d. What is the average height of the two teams in inches? a. 76 b. 78 c. 72 d. 75 If you were to join any of these two teams, which team would you choose? Why?12. Electra Company MEASURES each cable wire as it comes off the product line.

6 The lengths in centimeters of the first batch of ten cable wires were: 10, 15, 14, 11, 13, 10, 10, 11, 12 and 13. Find the standard deviation of these lengths. a. b. c. d. What is the variance in item 12? a. b. c. d. Items 14 video shop owner wants to find out the performance sales of his two branch stores for the last five months. The table shows their monthly sales in thousands of A2018181917 Branch B17152517184766111216 Feet and inches 6' 6'1" 6'4" 6'4" 6'6" 5'7" 6' 6'4" 6'4" 7' inches 72 73 76 76 78 67 72 76 76 8444814. What are the average sales of the two stores? a. 18 b. c. 19 d. Which store is consistently performing?

7 Why? For items 16 20 refer to the data below. Choose the letter that corresponds to the best answer:ClassFrequency46 50141 45236 40331 351026 30621 25916 20511 1566 1041 52 16. What is the class size? a. 4 b. 3 c. 5 d. 6 17. What is the value of the median score? a. b. c. d. 18. What is the range of the given set of data? a. 50 b. c. d. 19. What is the variance? a. b. c. d. 20. What is the standard deviation? a. b. c. d. LEARNING GOALS AND TARGETS After this lesson, you are expected to:a. demonstrate understanding of the key concepts of the different MEASURES of TENDENCY and MEASURES of variability of a given compute and apply accurately the descriptive MEASURES in statistics to data analysis and interpretation in solving problems related to research, business, education, technology, science, economics and others.

8 449 What to KnowWhat to Know Let us begin with exploratory activities that will introduce you to the basic concepts of MEASURES of CENTRAL TENDENCY and how these concepts are applied in real of CENTRAL TENDENCY of Ungrouped DataLesson Activity 1 contains familiar exercises provided to you in your Grade 7 modulesWHAT S THE STORY BEHIND?Activity 11. Daria bought T-shirts from a department store. She paid an average of Php 74 per shirt. Part of the torn receipt is shown below. a. How much did she pay for each white shirt? b. How much did she pay in all? Why? 2. The bar chart shows the number of magazines borrowed from the library last week. 450a. How many magazines were borrowed on Friday? Why? b. What is the average number of magazines borrowed per day last week? What does this value tell you? Why? `c. On what day is the most number of magazines borrowed?

9 Why? d. Describe the number of magazines borrowed on a Tuesday. Why do you think so? 3. The graph below shows the percentage of survey respondents reporting that they are satisfied with their current job. The horizontal axis is the years of schooling for different respondents. a. What information can be obtained from the graph? b. What conclusion can be made? Why? c. What made you say that your conclusion was correct? d. What necessary adjustment could be made to provide accurate information based on the graph? MEAL DEALA ctivity 2 To cater to five hundred (500) students having snacks all at the same time, your school canteen designed three meal package for the students to choose from. The monitors of each section were tasked to collect the weekly orders of each student. 451 MEAL 3=====================Item PriceHotdog Sandwich Salad Fries 2=====================Item PriceBaked Mac Bread Salad 1=====================Item PriceHamburger Fries : Form yourselves into groups.

10 Distribute to each member of the group the three meal packages. Make a week list of your preferred meal package. Record your group s order for the week on the sheet of paper below. Discuss with your group mate the answer to the questions below. Meal PackageDAILY MEAL PACKAGE PREFERENCE1 MondayTuesdayWednesdayThursdayFridayTota lSales23 TotalSalesA. In your group, 1. what is the most preferred meal package? 2. how much was the canteen s daily sales from each package? weekly sales? B. If all the groups will summarize their report,3. what might be the average weekly sales of the school canteen on each type of package?4. explain how these will help the canteen manager improve the sales of the school canteen. the combination of the food in each package. C. Make a combination of the food package of your choice. QUESTIONS?452 What to ProcessWhat to Process Here are some enabling activities/experiences that you will perform to validate your understanding on averages in the What to Know phase.