MEASURES OF CENTRAL TENDENCY AND MEASURES OF VARIABILITY

[Pages:64]MEASURES OF CENTRAL TENDENCY AND MEASURES OF VARIABILITY

I. INTRODUCTION AND FOCUS QUESTIONS

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?

443

Purefoods TJ Giants | 2007-08 PBA Philippine Cup Stats



In this module you will find out the measures of central tendency and measures of variability. 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? In this module, you will examine these questions when you study the following lessons.

II. 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 Data

444

In these lessons, you will learn to:

Lesson

Objectives:

1 ? Find the mean, median, and mode of ungrouped data ? Describe and illustrate the mean, median, and mode of ungrouped data

? Discuss the meaning of variability

? Calculate the different measures of variability of a given ungrouped data:

2

range, standard deviation, and variance

? Describe and interpret data using measures of central tendency and

measures of variability

3

? Find the mean, median, and mode of grouped data ? Describe and illustrate the mean, median, and mode of grouped data

? Discuss the meaning of variability

? Calculate the different measures of variability of a given grouped data:

4

range, standard deviation, and variance

? Describe and interpret data using measures of central tendency and

measures of variability

MMoodduullee MMaapp

Here is a simple map of the lessons that will be covered in this module.

Descriptive Statistics

Ungrouped Data

Grouped Data

Measures of Central Tendency

Measures of Variability

Measures of Central Tendency

Measures of Variability

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 lesson. 3. Have your own scientific calculator. Make sure you are familiar with the keys and

functions in your calculator.

445

III. 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 b. median

c. mode d. range

2. The most reliable measure of variability is _______________ .

a. range b. variance

c. average deviation d. standard deviation

3. For the set of data consisting of 8, 8, 9, 10, 10, which statement is true?

a. mean = mode b. median = mode

c. mean = median d. mean < median

4. Which measure of central tendency is greatly affected by extreme scores?

a. meanc. mode b. median d. none of the three

5. 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 b. 77

c. 78 d. 79

6. What is the median age of a group of employees whose ages are 36, 38, 18, 10 16 and 15 years?

a. 10 b. 15

c. 16 d. 17

7. Nine people gave contributions in pesos 100, 200, 100, 300, 300, 200, 200, 150, 100, and 100 for a door prize. What is the median contribution?

a. Php 100 b. Php 150

c. Php 175 d. Php 200

446

8. 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 b. 173

c. 174 d. 180

9. If the range of a set of scores is 14 and the lowest score is 7, what is the highest score?

a. 21 b. 24

c. 14 d. 7

10. What is the standard deviation of the scores 5, 4, 3, 6 and 2? a. 2 b. 2.5 c. 3 d. 3.5

11. What is the average height of the two teams in inches?

64 7

611 12

16

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

a. 76 b. 78 c.

67

72 76 76

84

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. 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. 1.7

b. 1.8

c. 11.9

d. 10.9

13. What is the variance in item 12?

a. 3.4

b. 3.3

c. 3.24

d. 2.89

For Items 14 ? 15.

A 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 pesos.

Branch A

20

18

18

19

17

Branch B

17

15

25

17

18

447

14. What are the average sales of the two stores?

a. 18 b. 18.4

c. 19

d. 19.5

15. Which store is consistently performing? Why?

For items 16 ? 20 refer to the data below. Choose the letter that corresponds to the best answer:

Class

Frequency

46 ? 50

1

41 ? 45

2

36 ? 40

3

31 ? 35

10

26 ? 30

6

21 ? 25

9

16 ? 20

5

11 ? 15

6

6 ? 10

4

1 ? 5

2

16. What is the class size?

a. 4 b. 3 c. 5 d. 6

17. What is the value of the median score?

a. 24.10

b. 24.29

c. 24.15

d. 24.39

18. What is the range of the given set of data?

a. 50

b.

19. What is the variance?

50.5

c. 49.5

d. 99.5

a. 119.59 b. 119.49 c. 119.40 d. 119.50

20. What is the standard deviation?

a. 10.90

b. 10.91

c. 10.92

d. 10.93

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 data.

b. 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.

448

Lesson

1 Measures of Central Tendency of Ungrouped Data

WWhhaatt ttoo KKnnooww

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 life.

Activity 1 contains familiar exercises provided to you in your Grade 7 modules

Activity 1 WHAT'S THE STORY BEHIND?

1. 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.

449

a. 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? 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?

Activity 2 MEAL DEAL

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.

450

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download