(STATISTICS AND PROBABILITY)

CONTENT STANDARD:

In this module, the learner is able to demonstrates understanding of key concept, uses

and importance of Statistics, data collection/gathering and the different forms of data

representation

LESSON AND COVERAGE:

LESSON LEARNING COMPETENCIES

1

Introduction to Statistics The Learner is able to explain the

basic concepts, uses and

importance of Statistics.

The Learner is able to poses

questions and problems that may

be answered using Statistics

2

The Tabular Presentation of Data

( ungrouped and grouped data)

The Learner is able to collects or

gathers statistical data and

organizes the data in a frequency

table according to systematic

consideration.

The Learner is able to analyzes,

interprets accurately and draws

conclusions from tabular data.

3

The Graphical Presentation of

Data

The Learner is able to Use

appropriate graphs to represent

organized data: pie chart, bar

graph, line graph and a

histogram.

The Learner is able to analyzes,

interprets accurately and draws

conclusions from graphic data.

4

Measure of Central Tendency

The Learner is able to find the

mean, median and mode of

statistical data. The Learner is able to describe

the data using information from

the mean, median and mode.

STATISTICS AND PROBABILITY

Introduction to Statistics

Presentation of Statistical Data

Tabular Presentation Graphical Presentation

Grouped

Data Ungrouped

Data Pie Chart

STATISTIC

S

Bar Graph

Line Graph

Histogram Measure of Central Tendency (Mean, Median, Mode)

This will guide the learner understand the flow of

discussion.

1. A general term used to summarize a process that an analyst, mathematician or

statistician can use to characterize a data set.

a) Chart c)Histogram

b) Statistics d)Tabular presentation

2. Given the mean of 2, 7,8,10 and x is 6. Find the value of x.

a) 3 c)5

b) 7 d)8

3. What is the median of 60, 62, 71, 65, 71, 79, 71, 69, 78

a) 71 c)75

b) 70 d)69

Use the following information for questions 4&5

Marian’s math score from September to the end of November are as follows:

85%, 90%, 74%, 85%, 70%, 85%, and 75%

4. What is the mode of Marian’s math scores:

a) 70% c)85%

b) 74% d)90%

5. What is the mean of Marian’s math score’s

a) 65% c)72%

b) 81% d) 74%

6. The frequency table shows that the test results of a group of students.

Results Frequency

average 45

Pass 35

Fair 13

Fail 7

If the data is shown on a pie chart. Calculate the angle of a sector representing

students who obtained pass results.

7. The table shown the marks obtained by 9 participants in a mathematics quiz.

Find the difference between the mode and the median.

a) 0 c) 2

b) 1.4 d) 3

Direction: Encircle the best answer of the following

a) 35 ° c) 72°

b) 126° d) 162°

3 7 4 3 5 2 3 6 7

8. It is the middle value in distribution when the values are arranged in ascending or

descending order.

a) mean c) median

b) central tendency d) mode

9. What is the mean of the following set of numbers: 8, 4, 1, 7

a) 4 c) 1

b) 5 d) 2.5

10. In the set of data 2, 4, 5, 9, 10 and 11. 7 is the__________.

a) frequency c) median

b) mode d) mean

11. Each part of a pie chart that represents a group of data is known as__________.

a) a shaded region c) a segment

b) an angle d) a sector

12. A line graph is suitable to represent data collected over a period of time. Which of the

following data is suitable to be represented by line graph?

a) Number of students who scores A in mathematics test

b) Amount of rainfall recorded in a year.

c) The price of imported cars.

13. What is the mean of: 6, 4, 10, 1, 5, and 4?

a) 4 b) 5

b) 30 d) 6

Use this bar graph to answer questions 14-16.

14. How many records were sold on Wednesday?

a) 90 c) 100

b) 110 d) 120

15. In what two days were the same numbers of records sold?

a) Thursday and Friday c) Friday and Saturday

b) Monday and Wednesday d) Wednesday and Thursday

16. On which day were the least number of records sold?

a) Monday c) Tuesday

b) Wednesday d) Saturday

17. It is the sum of the value of each observation in a dataset divided by the number of

observations. This is also known as the arithmetic average.

a) Mean c) Median

b) Central tendency d) Mode

Records Sold in One Week

0

20

40

60

80

100

120

140

Mon. Tues. Wed. Thurs. Fri. Sat.

Day

Num

ber

of r

ecor

ds

Use the line graph to answer question 18-20

18. What was the total precipitation in December?

a) 16 mm c) 25 mm

b) 22 mm d) 20 mm

c)

19. What was the total precipitation in March and April together?

a) 24 mm c) 26 mm

b) 22 mm d) 20 mm

20. What month was the highest precipitation occurred?

a) April c) May

b) February d) August

21. It is the most frequent value occurs in a set of data.

a) Mean c) Central tendency

b) Median d) mode

22. The Lakers scored the following numbers of goals in their last twenty matches:

3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 3

Which number had the highest frequency?

a) 3 c) 4

b) 6 d) 7

23. The pie chart shows the amount of time each day that Geri spends on various

activities. If this information were displayed using a bar graph with hours on the vertical

axis, what would be the height of the bar for sleep?

a) 8 hrs. c) 7hrs.

b) 6 hrs. d) 5 hrs.

24. Which letter occurs the most frequently in the following sentence?

THE SUN ALWAYS SETS IN THE WEST.

a) E c) S

b) T d) W

25. 15% of the students in a school of Business Administration are majoring in Economics,

20% in Finance, 35% in Management, and 30% in human resource. The graphical

device(s) which can be used to present these data is (are)

a) a line graph c) only a bar graph

b) only a pie chart d) both a bar graph and a pie chart

26. The most common graphical presentation of quantitative data is a

a) Histogram c) bar graph

b) relative frequency d) pie chart

27. In constructing a frequency table , the approximate class width is computed as

a) (largest data value – smallest data value)/number of classes

b) (largest data value – smallest data value)/sample size

c) (smallest data value – largest data value)/sample size

d) largest data value/number of classes

The numbers of hours worked (per week) by 400 statistics students are shown below.

28. The class width for this distribution is _______.

a) 9 c) 10

b) 39 d) varies from class to class

29. The number of students working 19 hours or less

a) 80 c) 100

b) 180 d) 300

30. The percentage of students working 19 hours or less is

a) 20% c) 25%

b) 75% d) 80%

Number of

hours

Frequency

0 - 9 20

10 - 19 80

20 - 29 200

30 - 39 100

INTRODUCTION TO STATISTICS

OBJECTIVES:

DISCUSSION:

Students in the class have different heights. How many in this

class have the same height? What is the common measure of

height did the class have? How will you answer the following with

varied questions?

That questions regarding to the problem above can be answer by

Statistics.

Statistics is the collection of methods for planning

experiments, obtaining data and the organizing, summarizing, presenting, analyzing,

interpreting and drawing conclusions.

HOW STATISTICS WORK?

Statistics starts with a question, not with data or information.

Every time we use statistics to find the solution for a question.

Statistics are what the decision makers can use to reduce inappropriate outcome

by qualifying it.

All statistics are based on data.

Data are what we hear, see, smell, touch and etc.

Data requires measuring.

Good measurement gives good data

Good data give better answer than bad data

But all data will give you all answer.

Statistics are designed to transform data to into information.

Statistics are about and used to measure/ assess risk of the decision.

In this lesson, the learners will able to;

Explain the basic concepts, uses and importance of Statistics.

Pose a questions and problems that may be answered using Statistics

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Directions: From the previous questions regarding the measurement of the

class heights. Answer and do the following.

How many in this class have the same height?

What is the common measure of height did the class have?

Instructions:

1. Using a tape measure or a meter stick. Measure your individual height.use

centmeter unit of meter.Round off measures to nearest cm.

2. Group yourselves into 8 or 10 members. List down all raw data and present it in the

best of presentation you can. After 10 minutes present your output.

Questions:

1. What do these numbers represents?

2. How can we get clear and precise information from the numbers?

3. Is the numbers are meaningful for everyone? Why?

Directions: Make a survey in your school to find out what websites is

commonly used by the students in doing their homework and activities. Ask at

least 50 students and present your data using any methods.

AREAS WE USE STATISTICS

Directions: Make a survey in your community or barangay to find out how

many members in each family has and look for their profile. Ask at least 10

families, present your data and answer the following questions.

1. What is your opinion about having many members in the family? Or few members in

the family? Why?

2. Does the member in each family have contribution in developing good community?

3. How many families have good income? Do you think numbers affect the status in

the family?

4. What is the importance of statistics in our society?

I Learned That…….

THE TABULAR PRESENTATION OF DATA

22 25 24 25 20 19 17 21 25 22

18 24 19 23 25 26 27 29 30 31

29 26 25 24 23 18 21 20 27 26

29 25 23 22 19 21 34 16 18 33

OBJECTIVES

DISCUSSION:

Presentation of data is one of the most important parts of a statistical study that is why,

it is very necessary to make the presentation in most effective manner as possible.

Tabular Presentation- a mode of data presentation which is presented in a more

concise and systematic manner through frequency tables consisting vertical columns and

horizontal rows with headings describing these rows and columns.

Frequency Table- a table that shows the number of occurrences of a score or numerical

value in a set of data.

Types of Frequency Table

1. Ungrouped Frequency Table- where data are less than 30.

Example: Banjo made a survey on the marrying ages of a group of Filipinos. This is what he

was able to gather. (n< 30)

The above set of data can be organized into a frequency table from decreasing or increasing

array, showing the ages and the number of occurrences for each age.

In this lesson, the learners will able to;

Construct a frequency table to organize data in systematic way.

Analyze, interprets accurately and draws conclusions from tabular data.

15 14 16 15 18 17 9 12 5 10

16 13 12 11 21 35 39 38 27 29

30 3 4 25 26 29 30 22 24 29

23 21 20 14 15 16 17 18 24 9

4 5 38 33 32 31 28 25 17 15

TABLE OF MARRYING AGES OF SOME FILIPINOS

AGE TALLY FREQUENCY

34 / 1

33 / 1

31 / 1

30 / 1

29 /// 3

27 // 2

26 /// 3

25 /////-/ 6

24 /// 3

23 /// 3

22 /// 3

21 /// 3

20 // 2

19 /// 3

18 /// 3

17 / 1

16 / 1

N= 40

Where N is the number of people surveyed

2. Group Frequency Table- where data are more than 30.

Example: Mervin surveyed the ages of the first 50 visitors to Ocean Park. The following are

the results.(n>30)

PROCEDURE

1. First, we take note of the smallest and the biggest values in the set of data, and

compute for the range.

Range is the difference between the highest and the lowest numbers in a set of raw data. It

shows how varied the scores or values in a set of data. The bigger the value of the range, the

wider the gap between values or the more varied the numbers are. A small range value

indicates a more uniform set of data.

Directions: Make a frequency table for each set of data.

1. Number of children in each family in a certain barangay.

2. Scores of a grade 6 pupil in Math in one quarter.

In our example: Highest number 39

Lowest number - 3

2. Next, decide how big the class interval should be. We may group the ages into 34, 6, or

9 or any number by which the range, 36, is divisible. However, we must remember that

some details or information are lost when bigger intervals are used. Intervals of 10 to 15

are considered fine.

Let us take a CLASS INTERVAL SIZE of 4.

3. Construct the frequency table. Write the title above the table.

AGES OF THE 50 VISITORS TO OCEAN PARKS

AGE TALLY FREQUENCY

36-39 /// 3

32-35 /// 3

28-31 /////-// 7

24-27 /////-/ 6

20-23 ///// 5

16-19 /////-/// 8

12-15 /////-//// 9

8-11 //// 4

4-7 //// 4

0-3 / 1

N= 50

5 4 3 5 5 6 9 8 1

7 2 2 8 8 4 4 4 5

1 3 7 6 4 10 4 6 3

36

6

89 85 86 82 90 92 90

87 89 84 84 83 88 89

89 85 91 87 89 83 84

Directions: Make a group frequency table on the ages of participants to a vigil

on “Peace and Progress” for our country. Use an interval 3.

Directions: Do as directed.

Mr. Protacio is doing a study on the literacy rate of Filipinos. He found out many

Filipinos drop out of schools at a very young age in spite of free public elementary and high

school education. Most of them drop out because of poverty. Below are the ages at which

some Filipinos drop out of school.

a) Make a frequency table of the ages.

b) What do you think should be done to minimize the number of school drop-outs?

c) How can you contribute to the solution of this problem?

18 21 17 15 34 42 32

24 28 27 21 18 17 32

34 36 37 23 25 45 22

19 20 24 21 19 19 20

29 30 31 17 35 25 25

8 14 7 9 8 7 17 12 9 12

12 11 16 15 14 13 9 10 10 15

17 16 16 12 10 11 13 14 14 16

I Learned That…….

THE GRAPHICAL PRESENTATION OF DATA

OBJECTIVES:

DISCUSSION:

Another way of presenting data is through graphical presentation. It is a visual display of

data and statistical results. It is often more effective than presenting data in tabular form. There

are many different types of graphical representation and which is used depends on the nature

of the data and the type of statistical results.

Imagine you just did a survey of your friends to find which kind of movie they liked best:

We can show that on a bar graph like this:

http://www.mathsisfun.com/data/bar-graphs.html

Table: Favorite Type of Movie

Comedy Action Romance Drama SciFi

4 5 6 1 4

In this lesson, the learners will able to;

To use and identify appropriate graphs to represent organized data: Analyze, interprets accurately and draws conclusions from graphical

presentation.

BAR GRAPH –it uses vertical or horizontal bars or rectangle to show quantity. This kind of

graph is used to compare or contrast different sets of data simultaneously.

Directions: Answer these questions based on the bar graph.

1. What does the graph show?

2. About how much rainforest cover did the Philippines have in the year of 1990?

3. By how much did the Philippine rainforest cover decline from 1990 until year 2000?

4. What is the total decrease in land area from 1990 to 2015? Estimate.

5. What do you think are the causes of the decline in the land area of our rainforest? What

will be its effects on the future generations?

6. What can you do to help the rehabilitation of our forest?

The table below shows Sam's weight in kilograms for 5 months

The given table has been summarized through Line graph.

Sam's Weight

Month Weight in kg

January 49

February 54

March 61

April 69

May 73

LINE GRAPH –it is used to show trends or patterns in numerical values that change over

a period of time. Line graphs are particularly useful for identifying patterns and trends in

the data such as seasonal effects, large changes and turning points. It is also called as

Frequency Polygon.

QUESTION

1. What is the title of this line graph?

2. What is the range of values on the horizontal scale?

3. What is the range of values on the vertical scale?

4. How many points are in the graph?

5. What was the highest value recorded?

6. What was the lowest value recorded?

7. Did Sam's weight increase or decrease over time?

Directions: Answer these questions based on the Line graph.

1. About how many Filipinos were there in 1975; 1993; and in 2003?

2. What is the difference between the populations in years 1975 and 2014?

3. Using the average increase project, how many Filipinos will there be by year 2016?

4. What are the positive and negative effects of population increase in our country and

world?

5. Do you think populations have great contribution in growth of economic in our country?

REGIONAL POPULATION IN THE PHILIPPINES

Region Population(in Millions) Percent

Southern Tagalog 11.3

NCR 10.4

Central Luzon 7.7

Western Visayas 0.5

Region 6 5.8

Total: 35.7 M

To construct the pie chart follow these steps:

1. Express each given numerical data as a percent of the total quantity.

Example: 10.4 ÷ 35.7 = 29 = 29% NCR

2. Compute the corresponding angle of each part or allocation by multiplying each percent

value obtained by 360 degrees, since a circle has 360 degrees.

Example: 29% x 360 = .29 x 360 = 104.4 °

3. Draw the circle and label the parts.

Anna Survey her friend on what favorite movie they liked best

Table: Favorite Type of Movie

Comedy Action Romance Drama Sci-fi

4 5 6 1 4

From the data, she constructed a pie chart.

PIE CHART – it is used to show partitions or allocations of parts or shares. This graph is

used to show the composition of a whole, shown in percent distribution. It is also called as

Circle Graph.

The histogram shows the heights of 21 students in a class and it grouped into groups of width

5 inches.

How many students were greater than or equal to 60 inches tall? The number of students greater than or equal to 60 inches tall are shown in the bars

representing the groups 60-65, 65-70, 70-75 and 75-80. =5+2+3+1 = 11

A class carried out an experiment to measure the lengths of cuckoo eggs. The length of

each egg was measured to the nearest mm. The results are shown in the following histogram:

Height

(inches)

Range

Frequenc

y

(Students

)

50-55 4

55-60 6

60-65 5

65-70 2

70-75 3

75-80 1

Length

( mm)

Range

Frequency

(cuckoo egg)

19-20 4

20-21 6

21-22 5

22-23 2

23-24 3

24-25 1

HISTOGRAM - it is a bar graph that shows how frequently data occur within certain

ranges or intervals. The height of each bar gives the frequency in the respective interval.

The range of each bar is also called the Class Interval.

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How many eggs were measured altogether in the experiment?

The number of eggs measured is found by adding the frequencies

= 1 + 8 + 17 + 40 + 26 + 8

= 100

How many eggs were less than 23 mm in length?

The number of eggs less than 23 mm in length is found by adding the frequencies for the

groups 19-20, 20-21, 21-22, and 22-23.

=1 + 8 + 17 + 40

= 66

Directions: Construct graphs for the following.

1. The Grade 5 classes supported the book drive of their school. They collected their old

books and donated them to schools in far flung areas. Construct a bar graph for their

collection.

2. Conduct a survey on any of the following topics and present the results in a bar graph.

a. Top problem of our country

b. Top problem of our youth

c. Preferred course in college

d. Preferred school or university in college

e. Preferred activity of the youth during leisure time

Directions: Do as directed.

Research on the monthly peso/ dollar exchange rate from previous year 2014. Record

the rates and present the trends through line graph or frequency polygon. Discuss the results

in class. Answer the questions.

1. At what month was the exchange rate at its highest? Lowest?

2. If dollar exchange rate is very high, what does it mean? What are its effects on our

economy?

3. What could be the possible reasons why the peso/ dollar exchange rate

increase/decrease?

4. Do you favor a high exchange rate or a low exchange rate? Explain your answer.

5. Who would likely favor a high peso/dollar exchange rate?

Grade 5-A 550 books

Grade 5-B 700 books

Grade 5-C 600 books

Grade 5-D 850 books

Grade 5-E 1000 books

Directions: Do the following.

1. Construct a pie chart for the following. Show computations of percent and angle

distributions using the given data on a family monthly budget.

Food 9000

Rent 7500

Kids 6000 Leisure 1500 Savings 3500

Gasoline 2500 Total:

30 000

2. Make your own family budget and construct a pie chart to show it. Discuss the

results in class. What will be your priority in your budget? Should you spend

beyond your means? Why/Why not?

I learned that……

MEASURE OF CENTRAL TENDENCY

OBJECTIVES:

DISCUSSION:

After organizing a set of data, computation of some numerical information are needed

to interpret the gathered data. A measure of central tendency is a measure that used to

describe data. Mean, median and mode are the measure

Example 1: Hernandez took 7 math tests in one marking period. What is the mean test score?

Solution: 89 + 73 + 84 + 91+ 87+ 77+ 94= 595 ÷ 7 = 85

Answer: the mean test score is 85.

Example 2: A booklet has 12 pages with the following numbers of words: 271, 354, 296, 301,

333, 326, 285, 298, 327, 316, 287 and314. What is the mean number of words per page?

Solution: = 271 + 354 + 296 + 301 + 333 + 326 + 285 + 298 + 327 + 316 + 287 + 314

= 3,708 ÷ 12 = 309

Answer: the mean number of words per page is 309.

Example 3: A marathon race was completed by 5 participants in the times given below. What

is the mean race time for this marathon? 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr

Solution: 2.7 + 8.3 + 3.5 + 5.1 + 4.9 = 24.5 ÷ 5 = 4.9

Answer: The mean race time is 4.9 hr

Example 1: The Doran family has 5 children, aged 9, 12, 7, 16 and 13. What is the age of the

middle child?

Solution: Ordering the children’s' ages from least to greatest, we get

7, 9, 12, 13, and 16 (Odd set of data)

Answer: The child’s age in middlemost number of the data set is 12.

In this lesson, the learners will able to;

Find the mean, median and mode of statistical data. Describe the data using information from the mean, median and mode.

Give the importance of measure of central tendency in statistics.

MEAN- it is the average of a set of data. To calculate the mean, find the sum of the data

of and then divide by the number of data.

Mean = Sum of data values / number of values

MEDIAN-is the "middle" value in the set of data. The median is also the number that is

halfway into the set. To find the median, the data should be arranged in order from least

to greatest.

Example 2: A booklet has 12 pages with the following numbers of words: 271, 354, 296, 301,

333, 326, 285, 298, 327, 316, 287 and 314. What is the mean number of words per page?

Solution: Ordering the data from least to greatest, we get

=271, 285, 287, 296, 298, 301, 314, 316, 326, 327, 333, 354

= 301+ 314 = 615 ÷ 2 = 307.5

Answer: the median number of words per page is 307.5 since the set of data is even numbers.

Example 3: During the first marking period, Nicole's math quiz scores were 90, 92, 93, 88, 95,

88, 97, 87, and 98. What was the median quiz score?

Solution: Ordering the data from least to greatest, we get

= 87, 88, 88, 90, 92, 93, 95, and 96

= 90+92 = 182 ÷ 2 = 91

Answer: The median quiz score was 91 since the set of data is even numbers.

Example 1: The following is the number of problems that Ms. Matty assigned for homework on

10 different days. What is the mode? 8, 11, 9, 14, 9, 15, 18, 6, 9, 10

Solution: Ordering the data from least to greatest, we get:

= 6, 8, 9, 9, 9, 10, 11, 14, 15, 18,

Answer: The mode is 9

Example 2: In a crash test, 11 cars were tested to determine what impact speed was required

to obtain minimal bumper damage. Find the mode of the speeds given in miles per hour below.

24, 15, 18, 20, 18, 22, 24, 26, 18, 26, 24

Solution: Ordering the data from least to greatest, we get

= 15, 18, 18, 18, 20, 22, 24, 24, 24, 26, 26

Answer: Since both 18 and 24 occur three times, the modes are 18 and 24 miles per hour.

This data set is bimodal.

Example 3: A marathon race was completed by 5 participants. What is the mode of these

times given in hours? 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr

Solution: Ordering the data from least to greatest, we get

= 2.7, 3.5, 4.9, 5.1, 8.3

Directions: Do as directed.

1. Find the mean of the following numbers:

a) 82 84 86 88 90 92

b) 15 16 17 18 19 20 21 What do you notice?

2. Find the median and the mode of the following numbers:

5,7,12,6,8,9,11,10,7,6

MODE- it is the value in the set of data that occurs most often. If no number is repeated, then there is no mode for the list.

Answer: since each value occurs only once in the data set, there is no mode for

this set of data.

Directions: Compute for the mean, median, mode and the range of the

following numbers.

Mean Median Mode Range

1. 5,6,7,8,9,10,11,12,13

2. 3,3,3,3,3,3,3

3. 90,92,94,96,98,100

4. 1,1,2,2,3,3,3,4,4,4,5,5

5. 1,2,3,4,5,6,7,8,…39,40

6. 82,85,85,84,87,89,86,85

7. 200,350,500,650,800

8. 16,16,18,18,15,14,13,12

9. 4,4,8,12,16,20,20,24

10. 8,10,12,14,16,18

1. Carlo’s score of 97 in his eight test in Math made his mean score 90 in all the eight

tests. What was his mean score before he received his score of 97?

2. A bus which travelled for 6 days covered a mean distance of 140 km. if it traveled the

following distances: 180 km, 90 km, 100 km, 160 km. find the distance covered by the

bus on the sixth day.

3. Krista got the following scores: 93,96,90,97, 92. What should she get in her next quiz so

that her mean score will be 93?

4. Jong averaged 7 km in jogging for 6 days. What must be the distance he should cover

on the seventh day to have a mean distance of 8 km?

5. The mean scores is 85. If the tenth score is 90, find the mean of ten scores.

Directions: Solve the following problems.

PRETEST POST TEST

1. B

2. A

3. A

4. C

5. B

6. B

7. B

8. C

9. B

10. C

11. D

12. B

13. B

14. C

15. A

16. C

17. A

18. D

19. A

20. D

21. D

22. A

23. C

24. C

25. D

26. A

27. A

28. C

29. C

30. C

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

http://www.mathsisfun.com/data/histograms.html

www.ask.com › Math › Data Graphs

http://www.yourdictionary.com

http://www.proje115.ir

http://www.regentsprep.org/regents/math/algebra/AD2/measure.htm

http://www.clipartoday.com/freeclipart/school/school/oldbook_10937.html

http://www.purplemath.com /meanmode.htm

http://www.mathgoodies.com/lessons/vol8/mean.html

http://www.slideshare.net/roszelan/statistic-ii?