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The Average Scores of Grade 10A Students in Semester 1 Are Recorded in the Following Table:

D. Application activities:

Given two data tables as follows:

Table 1: The average scores of 10A students in semester 1 are recorded in the following table:

Average score

[0;5.0)

[5.0;6.5)

[6.5;8.0)

[8.0;10.0)

Frequency

0

6

19

15

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Table 2: The academic rankings of 10A students in semester 1 are recorded in the table below:

Academic ranking

Weak

Medium

Rather

Good

Frequency

1

6

18

15

Choose the appropriate chart type for each data table above, explain why, and draw a chart for each table.

IV. Lessons learned from teachers

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Da Nang, date…… month…… year……

APPROVED

Lesson 2: CHARACTERISTICS FOR MEASURING CENTRAL TREND ON COLUMN CHARTS AND HISTOGRAM CHARTS

I. OBJECTIVES 1. Knowledge:

Through this lesson, students will:

- Recall the knowledge about mean, median and mode learned

- Know some notes about qualitative charts can not find median, mean and mode

- Find the mean, median and mode based on the graph.

- Find the relationship between mean, median and mode values ​​based on the shape of the graph.

2. Skills

- Based on the histogram, determine the mean, median and mode.

- Determine the shape of the graph, from there, find the relationship between the mean, median and mode values.

3. Attitude

Enthusiastic and self-motivated in learning.

4. Orientation of capacity and quality

- Competence: self-study ability, problem-solving ability, cooperation ability, language ability.

- Qualities: Confident, independent.

II. PREPARATION

a. Teacher: Lesson plan, colored chalk,

III. ORGANIZING TEACHING ACTIVITIES

1. Stabilize the class: Check attendance

2. Check old lesson (no test)

3. Lesson progress:


Teacher's activities

Student activities

Content of the post

A. STARTUP ACTIVITIES

Objective : Review how to find the mean, median and mode learned in Algebra 10

Content : Give some exercises and ask students to find the mean, median and mode.

Example 1 : Given the following data on the ages of students in an English class: 10, 15, 13, 17, 18,

65, 20, 19, 22, 16, 21, 14

Find the mean and median of the above data series.

How to calculate the average of the above data series?


?So how is the median calculated?


?A friend standing in place helps her rearrange the data series above in order from smallest to largest.


?After arranging the above data series in order from smallest to largest, what is the median of the above series?


Example 2: Average score

-Students follow up


-Students read the requirements of Example 1


Student answer: To find the average , we add up all the values ​​of the elements of the sequence and then divide by the total number of elements.


Student answer: To calculate the median , first we arrange the data values ​​in order from smallest to largest.

If the number of elements in a sequence is odd, then the median is the middle number.

If the number of elements in the sequence is even, the median is the average of the two middle numbers.


Students stand in place and arrange the data series.

10, 13, 14, 15, 16, 17,


Example 1 : Given the following data on the ages of students in an English class: 10, 15, 13, 17, 18, 65, 20, 19,

22, 16, 21, 14

Find the mean and median of the above data series.

Prize

- Medium:


= 20.83


- Median:

Arrange the values ​​in order from smallest to largest:

10, 13, 14, 15, 16, 17, 18,

19, 20, 21, 22, 65

We see that there are 12 values ​​(observations) here, so the median of this sequence is the average of the two middle numbers, which are the sixth and tenth values.

Saturday.

-The teacher gives some examples of many types of data and asks students to find the mean, median, and mode.

are given in the following table.

18, 19, 20, 21, 22, 65


The above series has 12 values ​​so the median is the average of the 6th and 7th values.


Students read the question


The average score of the students is 8.3.

The median is 8.0


For the mean, we multiply the value by the corresponding frequency, then add the results and divide by the number of values.


For the median: Since the table has 11 values, the median is the 6th value which is 8.0


Students answer: First, 3 students read the requirements of Example 3.


Student answer: Convert the frequency distribution table to a class.

Median: (17+18) / 2 =

17.5


Example 2:


Average score:




Median:

Since N = 11, the median of this table is the value in the 6th position.

The value at position 6 is 8.0

So the median is 8.0


Mode: M 0 = 3


Example 3: In a high school, to find out the math learning situation of class 10A, people gave that class

m

7.5

7.8

8.0

8.4

9.0

number

1

2

3

2

2

Calculate the average score of the students. Find the median and mode of the table above.


?A friend helped her find the students' average score and median.


? Please present how to find the average and median for this data table for the whole class to listen.


What is the trend of the above data table?

Example 3: In a high school, to find out the math learning situation of class 10A, people let that class take a math test with the same test and create the following frequency distribution table for grouping classes.

subjects of 11 students

?If given the above frequency distribution table, how to find the mean and median?

?How to convert a clustered frequency distribution table into a discrete frequency distribution table?

?A friend stands in place and reads the representative values ​​of each class for the teacher?

After creating a discrete frequency distribution table, a friend helped her find the mean and median.


Problem statement: Above are problems in which we can determine the mean, median and mode based on a data table.

So if the requirement to determine those values ​​is based only on bar charts or

histogram then we

into a discrete frequency distribution table and then find the mean and median as in Example 2.


Student answer: Find the representative values ​​for each class as the average of the two endpoints of the corresponding class, and keep the frequency the same.


Student answer: The representative values ​​are 1; 3; 5; 7; 9. Student answer:

Mean: Median:

Take the Math test with the same test and create the following combined class frequency distribution table.

Prize

Discrete frequency distribution table

Price

treat

1

3

5

7

9

Frequency

number

2

4

12

28

4


Medium:


Median:

We see that there are 50 values, so the median is the average of the values ​​at positions 25 and 26. The value at position 25 is 7.

The value at position 26 is 7

So the median is 7


Let's get into today's lesson.



B. KNOWLEDGE FORMATION ACTIVITIES

Activity 1 : Review the concepts and meanings of mean, median and mode.

Objective : Students remember what they have learned.

Content : Presents theoretical parts and has examples at the level of recognition and understanding.

The teacher takes turns reviewing the concepts of mean, median and mode.

- Average value:

- For a series of discrete data, what is the formula for calculating the average value?

- For a discrete frequency table, what is the formula for calculating the mean?

- Median value:

?A friend reminded me how to find the median of a series of numbers.

- Mode: The mode M o is the value with the largest frequency in the frequency distribution table.

If in the frequency distribution table there are two values ​​with equal frequencies and greater than the frequencies of other values, then we have two values ​​that are bimodal.

- The meaning of value


Students think and answer: Take the sum of the values ​​and divide it by the number of values.


Student answer: Find the product of each value and the corresponding frequency, then take the sum of those results and divide it by the total number of elements.


-Students state how to find the median.


HS answer: The mean and median values ​​are taken as representative values ​​for the data set.


Students think but cannot answer

1. Review knowledge

- Average value:

- The average value of a series of numbers is

calculated by the formula:



-When given a discrete frequency distribution table


Price

treat



…


Frequency

number



…


The average value is calculated using the formula

- Median:

The median M e of a series of n unordered statistical data

decrease (or no increase) is

how to do

?Who can state the meaning of mean and median?

?So both mean and median values ​​are taken as representative values ​​for the data set, why does the median value still appear when there is a mean value?

From here, the teacher gives attention: Attention : For data with values ​​that are different from the remaining values ​​in an unusual way,

In the case of outliers (also called mean values ), the mean cannot represent the characteristics of the series. In this case, the median value represents the characteristics of the series better.

The teacher gives some examples to clearly describe the Note

In Example 2 and Example 3 : the values ​​do not differ too much so the mean and median values ​​are approximately the same.

In Example 1 : 65 is considered an outlier, because it is larger than the remaining values ​​by one.

unusual way. And it pulls


-The middle number of the sequence (the nth term ), if n is odd.

-Average of two

the middle number of the sequence (the and th term ), if n is even.


- Mode: The mode M o is the value with the largest frequency in the frequency distribution table.

If in the frequency distribution table there are two values ​​with equal frequencies and greater than the frequencies of other values, then we have two values ​​that are bimodal.


- Meaning of mean and median

Both of these quantities are intended to measure the central tendency of a data set.

Note : For data with values ​​that differ abnormally from the rest(also called outliers), the mean value cannot represent the characteristics of the series.

Then the median value is again

mean and median

this case


represents the characteristics of the series better.

Activity 2: Find the mean and median values ​​shown in the qualitative value chart.

Objective : Students understand that on qualitative charts, they cannot determine the mean value.

mean and median

-Teacher gives homework:

Exercise 1: The following graph shows the birthplaces of students in an introductory statistics course.

Determine the median. Teacher explains:

- We know that the median is the middle value of a set of data.

- The above chart consists of qualitative values, so we cannot find the median.

Teacher re-emphasizes knowledge

awake


Students think and answer


HS A: Median is Da Nang


HS B: More data is needed to find the median.


HS C: Cannot find the median


HS D: Median is Hue

2. Qualitative value chart For a chart consisting of qualitative values, we cannot find the mean and

median

The mean is quite different from the median (20.83 vs 17.5). Therefore, the mean cannot be used as a representative value in

Objective : Students can read data shown in the chart to find the average and median.

Point out some mistakes students make when determining the median based on the chart.

The teacher gives homework.

Exercise 2: A study was conducted to examine the living standards of families in a residential area. The following graph shows the distribution of family income of people in the residential area.


Find the median income of households in that neighborhood.


The teacher analyzes the students' answers and concludes:

In an organizational chart, the area of ​​the rectangles is proportional to the frequency (frequency) of the class. Therefore, when considering the distribution of data, people rely on the area of ​​the rectangles, not the


-Students think and answer


Student A: The median of income is 12 million because in the range of income values, 12 is the middle value.


HS B: The median income is between 12 and 14 million because in the chart above there are 8 columns, column 12-14 is in the middle position.


HS C: The median of income is 16 million because at the value of 16 we see it divides the data in half.


- From the chart, we can create a frequency distribution table.

- We need to move the board.

frequency distribution

3. Find the average, medianposition based on charthistogram :

Note: In an organizational chart, the area of ​​the rectangles is proportional to the frequency (frequency) of the class. Therefore, when considering the distribution of data, people rely on the area of ​​the rectangles, not on the height.

So the median in this case is the position that divides the area of ​​the graph in half.

Looking at the chart, we see that position 16 divides the area of ​​the chart in half.

So the median income of households in that residential group is 16 million.

Calculate the average and median income of households in that residential group.

Prize

From the graph, we have the distribution

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