Statistics, data presentation, frequency distribution, histogram, frequency polygon, frequency curve. Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.

2. Introduction
27, 25, 18, 20, 23, 27, 16, 19, 29, 26, 25, and 22 baht
Lunchtime spending of twelve students
Raw Data, Raw Score, or Observed Data
Quantitative Data
Amount of money Age Weight Distance
Qualitative Data
Gender Religion Favorite Sport Type of Accommodation

3. Statistical Methods
1. Constructing problems
2. Formulating questions
3. Collecting Data
4. Analyzing Data
5. Presenting Data
6. Interpreting Data
1. Questionnaires
2. Checklist
3. Interview
4. Tests
5. Evaluation Forms

4. Example
Baifern wanted to explore her family’s monthly phone bills. Therefore she
gathered all of the previous phone bills and made a table of data,
analyzed, and drew conclusions from the data.
Month Charge (Baht)
July 1,939.38
August 1,263.14
September 1,188.24
October 914.31
November 991.89
December 1,803.29
Total (6 months) 8,100.45

5. 1. Problem Monthly Phone Bills
2. Data Source Phone Invoices
3. Question How much was the phone bill each month?
4. Data Collection Taking notes from the documents
5. Type of Data Quantitative Data
6. Data Presentation Tabular presentation

6. 7. Interpretation The family spent the least amount of money on
phone bills in October and the most in July. They
cost 914.31 baht and 1,939.38 baht, respectively.
The phone bills were getting less expensive in the
first five months of the second half of the year.
However, it was as twice as expensive in December
compared to the previous month. On average, the
phone bill was 1,350 baht a month.
8. Decision-making Use the phone only when necessary to reduce
phone bill costs

7. 10
20
30
40
50
Mango Lime Tamarind Jackfruit Neem Others
Prices
(Baht)
Types of
Tree
Example
Punyathorn was interested in the prices of the trees sold by Chom. He
asked Chom for the prices of various trees, recorded the data, analyzed
them, and presented them in the bar chart shown below.

8. 1. Problem Price of grafted plants
2. Data Source Chom, the tree shop owner
3. Question How much was each type of tree?
4. Data Collection Interview
5. Type of Data Quantitative Data
6. Data Presentation Bar Chart

9. 7. Interpretation The prices for grafted plants varied from 25 – 50
baht depending on the type of plant . Tamarind and
Neem were the most expensive plants.
8. Decision-making Recommend parents, friends, and teachers to buy
from the tree shop

10. DATA COLLECTION
and
DATA PRESENTATION

11. Frequency Distribution of Data
Raw score, Raw data, or Observed Data
Data that have not gone through some systematic process to make them
easy to understand and interpret
Score of ten students for their homework
20, 24, 18, 19, 20, 15, 20, 22, 14, and 21
1. What is the lowest score obtained by a student?
2. How many students got less than 15?
3. How many students got a score from 16 to 20?

12. 20
Score of forty students for their homework
20 14 10 10 26 18 19 25 26
24 15 21 15 26 26 10 12 22 18
18 20 20 25 22 27 14 13 22 18
19 22 15 19 17 20 28 15 18 25
1. What is the lowest score obtained by a student?
2. How many students got less than 15?
3. How many students got a score from 16 to 20?

14. Frequency Distribution
The process in which the data in a set are
grouped according to their values and then
counted so that we have the number of
times each value appears in the data set.
These numbers of times are called
frequency.

15. From a survey on 25 students, it was found that the days of the week they
were born on were Wednesday, Sunday, Thursday, Wednesday, Monday,
Sunday, Saturday, Saturday, Wednesday, Friday, Tuesday, Saturday, Monday,
Sunday, Wednesday, Saturday, Thursday, Tuesday, Monday, Monday,
Thursday, Wednesday, Sunday, Tuesday, and Wednesday. Construct the
frequency table for this set of data and interpret the data.
Day of the Week Tally Frequency
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Total
4
4
3
6
3
1
4
25

16. The results (in seconds) from the 100-meter sprints of 40 students are as
follows:
12 13 13 15 14 14 13 13 12 13
13 15 14 14 12 15 13 14 13 14
12 12 13 14 14 14 12 13 13 13
13 14 12 14 13 15 12 14 14 13
Time (seconds) Tally Frequency
12
13
14
15
Total
8
15
13
4
40

17. The full score of Thai language exam is 15. Forty students in a class had
scores according to the following distribution table:
Score Tally Frequency
1 - 3 3
4 - 6 13
7 - 9 11
10 - 12 9
13 - 15 4
Total 40
Grouped Frequency Distribution
Class Interval
Class Interval Widths

18. The following distribution table shows the results from the survey of the daily
allowances of forty-one students in a classroom.
Allowance (Baht) Tally Frequency
10 - 19 2
20 - 29 8
30 - 39 15
40 - 49 10
50 - 59 4
60 - 69 1
70 - 79 1
Total 41
1) How many class intervals are there in the distribution table?
2) What are the widths of the class intervals 50 to 59 and 60 to 69?
3) Do all class intervals have equal widths?

19. The following distribution table shows the results from the survey of the daily
allowances of forty-one students in a classroom.
Allowance (Baht) Tally Frequency
10 - 19 2
20 - 29 8
30 - 39 15
40 - 49 10
50 - 59 4
60 - 69 1
70 - 79 1
Total 41
4) How many students have 40 to 49 baht daily allowances?
5) How many students have less than 30 baht of daily allowances?
6) How many students have more than 50 baht of daily allowances?

20. The following distribution table shows the results from the survey of the daily
allowances of forty-one students in a classroom.
Allowance (Baht) Lower Bound-Upper Bound Frequency
10 - 19 9.50 – 19.50 2
20 - 29 19.50 – 29.50 8
30 - 39 2.50 – 39.50 15
40 - 49 39.50 – 49.50 10
50 - 59 49.50 – 59.50 4
60 - 69 59.50 – 69.50 1
70 - 79 69.50 – 79.50 1
Total 41
The class interval 10 to 19 means all values from 9.50 to less than 19.5
9.50 is the lower bound of the class 10 to 19.
19.50 is the upper bound of the class 10 to 19.

21. Data Presentation Using
Histograms, Frequency Polygons,
Frequency Curves

22. The frequency distribution showing the weights of seventy-five
children in the village.
Allowance (Baht) Lower Bound Upper Bound Frequency
10 - 12 2
13 - 15 5
16 - 18 13
19 - 21 23
22 - 24 18
25 - 27 10
28 - 30 4
Total 75
9.50 12.50
12.50 15.50
15.50 18.50
18.50 21.50
21.50 24.50
24.50 27.50
27.50 30.50

23. 4
8
12
16
20
24
9.5 12.5 15.5 18.5 21.5 24.5 27.5 30.5
Number of students
Weight (kg)

24. Histogram Frequency polygon
Frequency curve

34. Lower Bound Upper Bound
4,000.5 7,000.5
7,000.5 10,000.5
10,000.5 13,000.5
13,000.5 16,000.5
16,000.5 19,000.5

35. 4
8
12
16
20
24
4,000.5 7,000.5 10,000.5 13,000.5 16,000.5 19,000.5

37. Lower Bound Upper Bound
25.5 30.5
30.5 35.5
35.5 40.5
40.5 45.5
45.5 50.5
50.5 55.5
56.5 60.5
61.5 65.5
65.5 70.5

38. 2
4
6
8
10
12
25.5 30.5 35.5 40.5 45.5 50.5 55.5 60.5
Number of students
65.5 70.5