Chapter 20 Data Analysis

Zhang Qinghua, Shahe Middle School, Ganyu County, Jiangsu Province

Curriculum standard requirements

Test center curriculum standards require knowledge and skill objectives.

Understand, understand and master flexible applications.

Group, individual, sample and sample size Understand the meaning of the concepts of group, individual, sample and sample size.

Average, mode and median Understand the meaning of average and weighted average, and find the average of a set of data.

Understand the role of mode and median.

Will find the mode and median of a set of data.

Range, variance and standard deviation Understand the concepts of range, variance and standard deviation.

Understand the role of range, variance and standard deviation.

Will find the range, variance and standard deviation of a set of data.

Knowledge carding

Several basic concepts of 1. solution statistics

Population, individual, sample and sample size are unique laws in statistics. Accurately grasping the teaching materials and making clear the object of investigation are the key to solve the problems related to the whole, individual, sample and sample size.

2. Average

When a given set of data fluctuates around a constant a, a simplified average formula is generally chosen, where a is a number close to the average value of this set of data. When there are duplicate data in a given set of data, the weighted average formula is usually used.

3. Mode and median

Mean, mode and median are all quantities used to describe the trend of data sets. The size of the average is related to every data, and the fluctuation of any number will cause the fluctuation of the average. When one data in a set of data is too high or too low, it is not appropriate to describe the overall trend with the average value, but it is more appropriate to use the median or the mode. The median is related to the arrangement of data, and the fluctuation of individual data has no effect on the median; When a group of data has a lot of repeated data, it can be described by patterns.

4. Extreme poverty

The difference between the maximum value and the minimum value in a set of data reflects the range of this set of data. The difference obtained by this method is called extreme value range, and extreme value range = maximum-minimum value.

5. Variance and standard deviation

The result of "average first, then difference, then square, and finally average" is used to indicate that a group of data deviates from the average. This result is called variance, and the calculation formula is

S2 =[(x 1-)2+(x2-)2+…+(xn-)2]；

Standard deviation =

Variance and standard deviation are both quantities that reflect the fluctuation of a set of data. The greater the value, the greater the fluctuation, the more unstable or irregular it is.

Ability training

First, fill in the blanks:

1.A, b and c three packaging machines package 400g tea at the same time. Randomly select 10 boxes from their respective tea packages, and measure their actual quality differences, as shown in the following table:

A packaging machine b packaging machine c packaging machine

discrepancy

(g 2) 3 1.96 7.96 16.32

According to the data in the table, it can be considered that the quality of tea packaged by packaging machine is the most stable among the three packaging machines.

2. Three machine tools A, B and C produce screws with a diameter of 60mm. In order to test the product quality, 20 screws produced by three machine tools were randomly selected for diameter measurement. After data processing, it is found that the average value of these three groups of data is 60mm, and their variances are S2 A =0. 162, S2 B =0.058, and S2 C = 0.65438.

3. The variance of a set of data: 2, -2, 0 and 4 is.

4. On the occasion of the arrival of World Environment Day, Hope Middle School held a seminar with the theme of "Environment and Human Survival", one of which was to make a social survey of our living environment and evaluate the students' survey reports. Grade 3 (3) Class collates the scores of 50 student survey reports of this class (scores are all integers), lists the frequency distribution table, and draws the frequency distribution histogram (part) as follows:

Packet frequency

49.5~59.5 0.04

59.5~69.5 0.04

69.5~79.5 0. 16

79.5~89.5 0.34

89.5~99.5 0.42

Total 1

Answer the following questions based on the above information:

(1) There are _ _ _ _ _ _ _ _ * investigation reports with 90 points or above in this class;

(2) the investigation report that the class was rated as excellent grade (80 points or above) accounted for _ _ _ _ _ _%;

(3) Complete the histogram of frequency distribution.

5. According to the data, the leaning tower of Pisa in Italy is inclined by 1. 1 mm every year on average during 4 1 year. During the period of 1959 ~ 1 1 year, the annual average dip angle is 1.26mm, so during the 52-year period of 19 18 ~ 1969, the annual average dip angle is.

6. In order to alleviate the drought, our city launched rockets to increase rainfall and implemented precipitation enhancement operations. In one rainfall, 65,438+00 areas with the same area were measured in a county, as shown in the following table:

Area 1 2 3 4 5 6 7 8 9 10

Rainfall (mm)10/213132015141565438.

Then the rainfall pattern in this 10 area of the county is _ _ _ _ _ _ _ (mm); The average rainfall is _ _ _ _ _ (mm).

7. An archer hits the target five times in a row, and the number of rings obtained is 8, 6, 10, 7 and 9 respectively, so the standard deviation of the number of rings obtained by the archer is _ _ _ _ _ _ _ _.

8. The following figure shows the completion of Taiyuan's total fiscal revenue from 2002 to 2004 published by Taiyuan Daily on February 25th this year. The data in the figure is accurate to 1 100 million yuan. According to the data in the figure, complete the following questions:

(1) The total fiscal revenue in 2003 was _ _ _ _ billion yuan higher than that in 2002;

(2) The annual growth rate of total fiscal revenue in 2004 was _ _ _ _ _ _ _; (accurate

To 1%)

(3) If the annual growth rate of total fiscal revenue in 2005 is not lower than that in 2004.

The annual growth rate of total fiscal revenue is expected to reach at least in 2005.

To _ _ _ one hundred million yuan. (accurate to 1 100 million yuan)

9. In order to investigate the traffic volume of a certain intersection at a certain time, the traffic police recorded the number of cars passing through the intersection at the same time in a week. The recorded situation is as follows:

Monday, 23456

Number of cars 100 98 90 82 100 80 80

Then the average number of cars passing through the intersection at that time this week is _ _ _ _ _ _ _ _ _ _ _.

10. Figure (1)(2) is the broken line statistics drawn according to the daily average temperature in a certain place in the first half of June in recent two years.

By observing the chart, we can judge the year when the temperature was relatively stable in the first half of June these two years.

Second, answer questions:

1. The following figure reflects the degree of satisfaction of the surveyed users with the after-sales service of A and B brands of air conditioners (hereinafter referred to as "user satisfaction"), which is divided into four grades: very dissatisfied, dissatisfied, satisfied and satisfied, which are recorded as 1, 2, 3 and 4 in turn.

(1) Calculate the average customer satisfaction scores of brand A and brand B respectively (the calculation result is accurate to 0.01);

(2) According to the histogram and the above calculation results, which brand has higher customer satisfaction? What is the brand's user satisfaction rating model?

2. As shown in the figure, the changes in the number of tourists in tourist attractions A and B from 2002 to 2006 are indicated by solid lines and dotted lines respectively. Answer the following questions according to the picture:

Compared with the previous year, in which year did the number of tourists in (1)B tourist spot increase the fastest?

(2) Find the average and variance of the number of tourists in tourist spots A and B from 2002 to 2006, and evaluate the situation of these two tourist spots in one sentence from the perspective of the average and variance;

(3) At present, the ticket price of tourist attraction A is 80 yuan per person. In order to protect the environment of tourist attractions and the safety of tourists, the best reception number of tourist attractions A is 40,000. In order to control the number of tourists, tourist attraction A decided to raise the ticket price. It is known that the ticket price X (yuan) satisfies the functional relationship with the number of tourists Y (ten thousand). If the number of tourists in tourist attraction A does not exceed 40,000, how much should the ticket price increase at least?

3. As shown in the figure, it is a broken-line statistical chart to test the physical training of two athletes, A and B, for ten weeks in a row. The coaching staff stipulates that the physical fitness test score of 70 or above (including 70 points) is qualified.

(1) Please fill in the following table according to the information provided in the picture:

Average physical fitness test score median qualified times

Jia 65

B 60

(2) Please judge the results of athletes' physical fitness test from the following two different angles:

① Comparing A and B according to the average number of times they passed the exam, their physical fitness test scores are better;

② Comparing A and B according to the average and median, their physical fitness test scores are better.

⑶ According to the statistical chart of broken line and the number of passing scores, analyze which athlete's physical training effect is better.

In order to help poor out-of-school children, a youth league committee launched a "love saving" activity to encourage students to deposit their lucky money and pocket money in the bank for a fixed period of one year. After the expiration, they can get back the principal and donate the interest to the poor children who are out of school. There are 1200 students in a middle school. Figure 1 is a fan-shaped statistical chart of the proportion distribution of students in all grades, and Figure 2 is the per capita deposit of students in our school.

(1) The per capita deposit of ninth grade students is RMB;

(2) What is the per capita deposit of students in this school?

(3) It is known that the annual interest rate of one-year fixed deposits in banks is 2.25%.

("Love savings" is exempt from interest tax), every 35 1 yuan can provide the basic expenses for one school year, so how many poor children can the school help in one school year?

Reference answer:

First, fill in the blanks:

1 . b； 2.b； 3.5; 4.2 1,76; 5. 1. 13; 6. 14, 14; 7.； 8.( 1) 19 (2)30%(3) 156; 9.90; 10.2005

Second, answer questions:

1.( 1) The number of users surveyed by brand A is 50+100+200+100 = 450 (households).

The number of users surveyed by Brand B is10+90+220+130 = 450 (households).

Average satisfaction score of a brand = ≈ 2.78.

The average score of brand satisfaction is B = ≈ 3.04.

A: The average scores of brand satisfaction of A and B are 2.78 and 3.04 respectively.

(2) The brand with higher customer satisfaction is brand B. ..

Because the average satisfaction score of brand B is large, and according to the statistical chart, there are more users of brand B who are "satisfied" and "very satisfied"; The customer satisfaction model of this brand is 3 points.

2. (1) The number of tourists in scenic spot B increased the fastest in 2005 compared with the previous year.

(2) = = 3 (ten thousand yuan)

= = 3 (ten thousand yuan) = [(-2)+(-1)+0+1+2] = 2.

= [0 +0 +(- 1) + 1 +0 ]=

From 2002 to 2006, the annual average number of tourists in tourist attractions A and B was 30,000, but the fluctuation range of tourists in tourist attraction A was greater than that in tourist attraction B. 。

(3) Get a solution of 5-≤ 4 from the meaning of the question, and x ≥ 100 100-80 = 20.

A: Tickets for tourist attraction A should be increased by at least 20 yuan.

3.( 1)

Average physical fitness test score median qualified times

A 60 65 2

57.5 4

(2)①B； ② A。

⑶ From the line chart, the physical fitness test scores of the two athletes are on the rise, but the growth rate of B is faster than that of A, and the number of qualified scores of B is more than that of A in the later period, so the training effect of B is better.

4.( 1) 240 (2) Solution 1:

Total deposit in the seventh grade: 400×1200× 40% =192,000 yuan.

Total amount of the eighth-level deposit: 300×1200× 35% =126,000 yuan.

Total deposit of Grade 9: 240×1200× 25% = 72,000 yuan.

(192000+126000+72000) ÷1200 = 325 (yuan)

Therefore, the per capita deposit of students in this school is 325 yuan.

Scheme 2: 400× 40%+300× 35%+240× 25% = 325 yuan.

Therefore, the per capita deposit of students in this school is 325 yuan.

(3) Scheme 1: (192000+126000+72000) × 2.25% ÷ 351= 25 (person)

Solution 2: 325×1200× 2.25% ÷ 351= 25 (human).