## Math 10 Chapter 5 Lesson 2: Charts

## 1. Summary of theory

### 1.1. Column histogram

To describe the frequency distribution table of classifiers, people erect vertical columns (contiguous or separate) whose width is equal to the length of the class, and the height of the column is equal to the frequency of the corresponding class.

### 1.2. Frequency curve

On the coordinate plane define the points \((C_i, f_i) i = 1, 2, 3, …\) where \(C_i\), is the representative value of the \(i\)th layer. , \(f_i\) is the frequency of the \(i\)th class. The bend line connecting the points \((C_i, f_i)\) in the order \(i = 1, 2, 3, …\) is the frequency curve.

**Attention: **The layered frequency distribution table can be described using a bar graph or frequency curve.

### 1.3. Fan chart

Draw a circle with center \(O\) and then draw fan shapes with vertices \(O\), the angle at the top is proportional to the frequency of the layers. Such a visual representation of a frequency distribution table is called a fan histogram.

**Eg:**

**Attention:** Layered frequency tables can also be depicted with a fan plot.

## 2. Illustrated exercise

**Question 1: **Given the following frequency distribution table:

The average temperature of December in Vinh city from 1961 to 1990 (30 years).

Describe Table 6 by plotting bar and column histograms and frequency curves.

**Verse 2: **Based on the fan diagram in Figure 37 below, make a table of the structure as shown in example 2.

(1) State-owned enterprise zone

(2) Non-state sector

(3) Foreign investment sector

**Solution guide**

Structure of domestic industrial production value in 1999, by economic sectors (%)

## 3. Practice

### 3.1. Essay exercises

**Question 1: **For fan charts

Based on the given fan charts, make a table showing the target structure of the Vietnamese people in 1975 and 1989.

**Verse 2: **Given the following table of frequency distribution and frequency of layering:

Average temperature of December in Vinh city from 1961 to the end of 1990 (30 years)

a) Calculate the average of tables 6 and 8.

b) From the results calculated in question a), what do you notice about the temperature in Vinh city in February and December (of the 30 years surveyed)

### 3.2. Multiple choice exercises

**Question 1: **Which of the following chart types is the most suitable for the representation of the frequency distribution table?

A. Fan chart

B. Column chart

C. Map Organizer

D. Frequency polygon plot

**Verse 2: **Which of the following chart types best shows a comparison of a component to the whole?

A. Column chart

B. Map Organizer

C. Frequency polygon plot

D. Fan chart

**Question 3: **Statistics of math test scores in an exam of 400 students. It was found that the number of papers with 10 points accounted for 2.5%. What is the frequency of the value xi = 10?

A. 10

B. 20

C. 25

D. 5

**Question 4: **To investigate the children in each family of a 100-family apartment complex. People selected 20 families on the 4th floor and obtained the following data sample:

2 4 2 1 3 5 1 1 2 3

1 2 2 3 4 1 1 2 3 4

How many different values are there in the sample data above?

A. 4

B. 20

C. 10

D. 5

**Question 5: **Statistics of math test scores in an exam of 400 students. It is found that there are 72 problems with a score of 5. What is the frequency of the value xi = 5?

A. 72%

B. 36%

C. 18%

D. 10%

## 4. Conclusion

Through this lesson, you should know the following:

- Recognize different types of charts.
- Know how to draw graphs.

.

=============