Statistics 8th Edition Jia Junping Chapter 3 after class exercises and answer summary

1. Examination site induction

One 、 Thinking questions

1 What does data preprocessing include ？

answer ： Data preprocessing is the necessary processing done before data classification or grouping , The content includes data review 、 Screening 、 Sort, etc .
（1） Data audit is to check whether there are errors in the data . For the original data obtained through the survey , Mainly from the integrity and accuracy of two aspects to audit ; For second-hand data obtained through other channels , We should focus on the applicability and timeliness of the audit data .
（2） Data filtering is to find a certain type of data that meets specific conditions according to needs .
（3） Data sorting is to arrange data in a certain order , So that researchers can find some obvious characteristics or trends by browsing the data , Find clues to solve the problem . besides , Sorting also helps check and correct data , And provide convenience for reclassification or grouping .

2 What are the sorting and graphic methods of classified data and sequential data ？

answer ：（1） Sorting and graphic method of classified data

① Sorting method of classified data ： First, list the categories of classified data , Then calculate the frequency of each category 、 Frequency or proportion 、 Ratio, etc , A frequency distribution table can be formed ;

② Graphic method ： Bar chart 、 Pareto Diagram 、 Pie chart and ring chart .

（2） Sorting and graphic method of sequential data

① Sorting method of sequential data ： First, classify the data in a certain order , Then calculate the frequency of each category 、 The proportion 、 percentage 、 Ratio, etc , For sequential data , In addition to the collation and graphic technology of classified data , You can also calculate the cumulative frequency and cumulative frequency （ percentage ）;

② Graphic method ： Bar chart 、 The pie chart 、 Pareto Diagram 、 Cumulative frequency distribution diagram and ring diagram .

3 What are the grouping methods of numerical data ？ Briefly describe the steps of group spacing and grouping .

answer ：（1） Data grouping methods include univariate value grouping and group distance grouping .

① Univariate value grouping is to take each variable value as a group , This grouping is usually only suitable for discrete variables , And the variable value is less ;

② In the case of continuous variables or more variable values , Group spacing is usually used . It divides all variable values into several intervals in turn , And take the variable values of this interval as a group . In the group spacing group , The minimum value of a group is called the lower limit ; The maximum value of a group is called the upper limit .
（2） Group spacing grouping steps

① Determine the number of groups . The determination of the number of groups should be aimed at displaying the distribution characteristics and laws of the data . In general , The number of groups of a group of data should not be less than 5 Group and no more than 15 Group , namely 5≤K≤15;

② Determine the group spacing of each group . Group distance is the difference between the upper limit and the lower limit of a group . The group distance can be determined according to the maximum and minimum values of all data and the number of groups , Group distance ＝（ Maximum － minimum value ）÷ Group number ;

③ Compile frequency distribution table according to groups .

4 What is the difference between a histogram and a bar chart ？

answer ： The difference between histogram and bar graph ：
（1） The length of the bar chart is used to indicate the frequency of each category , Its width is fixed ; Histogram is used to express the frequency of each group by area , The height of the rectangle indicates the frequency or frequency of each group , The width indicates the group spacing of each group , Therefore, its height and width are meaningful ;
（2） Due to the continuity of packet data , The rectangles of the histogram are usually arranged continuously , The bar chart is arranged separately ;
（3） Bar chart is mainly used to display classified data , Histogram is mainly used to display numerical data .

5 What problems should be paid attention to when drawing a line diagram ？

answer ： Attention should be paid to when drawing the line diagram ：
（1） Time is usually drawn on the horizontal axis , Observations are plotted on the vertical axis ;
（2） Generally, it should be drawn as a rectangle with the horizontal axis slightly larger than the vertical axis , Its length width ratio is approximately 10：7;
（3） The figure is too flat or too thin , Not only beautiful , And it will cause visual illusion , It is not conducive to the understanding of data changes ;
（4） In general , The lower end of the vertical axis data should be “0” Start , For comparison . If the data is consistent with “0” The spacing between them is too large , You can break the vertical axis with a broken symbol .

6 What is the difference between a pie chart and a ring chart ？

answer ： There is one in the middle of the ring chart “ empty ”, Each part of the data in the sample or population is represented by a segment in the ring . The pie chart can only show the proportion of each part of a sample or population , The ring chart can draw data series of multiple samples or populations at the same time , The data series of each sample or population is a ring , It is conducive to the comparative study of composition .

7 What are the advantages of stem and leaf graph compared with histogram ？ What are their applications ？

answer ：（1） Advantages of stem and leaf graph compared with histogram ： The stem leaf diagram is similar to the horizontal histogram , Compared with histogram , The stem leaf diagram can not only give the distribution of data , And can give every original value , That is, the information of the original data is preserved . Although histogram can well display the distribution of data , But the original value cannot be retained .
（2） Application of stem leaf diagram and histogram ： Histograms are usually suitable for large quantities of data , Stem and leaf charts are usually suitable for small batch data .

8 What are the criteria for identifying the advantages and disadvantages of charts ？ answer ： The criteria for identifying the advantages and disadvantages of graphics are ：
（1） A good picture should be carefully designed 、 It helps to gain insight into the essence of the problem ;
（2） A good picture should make complex ideas concise 、 exact 、 Efficient elaboration ;
（3） A good picture should be able to provide the reader with the largest amount of information in the shortest time with the least pen and ink ;
（4） A good picture should be multidimensional ;
（5） A good picture should describe the true situation of the data .

9 What problems should we pay attention to when making statistical tables ？

answer ： Pay attention to the following points when making statistical tables ：

（1） We should reasonably arrange the structure of the statistical table , Such as line Title 、 Column headings 、 The location of data should be arranged reasonably . Of course , Because the emphasis is different , Row headings and column headings can be interchanged , However, the horizontal and vertical length ratio of the statistical table should be appropriate , Avoid too high or too wide table forms .
（2） The header should generally include the table number 、 General title and units of data in the table . The general title should concisely and accurately summarize the contents of the statistical table , Generally, it is necessary to explain the time of statistical data （When）、 place （Where） And the content （What）, That is, the content of the title should meet 3W requirement . If all the data in the table are in the same UOM , It can be marked in the upper right corner of the table . If the unit of measurement of each variable is different , It should be placed after each variable or listed separately to indicate .
（3） The upper and lower horizontal lines in the table usually use thick lines , Other lines in the middle should use thin lines , This makes people look clear 、 Eye-catching . Usually , The left and right sides of the statistical table are not sealed , Column headings can be separated by vertical lines if necessary , Row headings are usually not separated by horizontal lines . All in all , Try not to use horizontal and vertical lines in the table . The data in the table is generally right aligned , If there is a decimal point, it should be aligned with the decimal point , And the number of decimal places should be unified ; For table cells without data , It's usually used “—” Express ; Blank cells should not appear in a filled statistical table .
（4） When using statistical tables , If necessary, add notes at the bottom of the table , Special attention should be paid to indicating the data source , To show respect for others' labor achievements , For readers' reference .

Two 、 Exercises 1 To evaluate the quality of after-sales service in the household appliance industry , Randomly selected by 100 A sample of families . The grades of service quality are respectively expressed as ：A． good ;B． good ;C． commonly ;D． Poor ;E． Bad . The results are shown in the table 3-4 Shown .
surface 3-4　 Quality table of after-sales service in household appliance industry

requirement ：
（1） use Excel Make a frequency distribution table .
（2） Draw a bar chart , Reflect the distribution of evaluation grades .
（3） Draw Pareto Diagram of evaluation grade .

Explain ：
（2） Make a frequency distribution table , As shown in the table 3-5 Shown .

surface 3-5　 Frequency distribution of service quality grade evaluation
（2） Draw a bar chart of the evaluation grade , Pictured 3-1 Shown .

chart 3-1　 Bar chart of evaluation grade
（4） Draw Pareto Diagram of evaluation grade , Pictured 3-2 Shown .

chart 3-2　 Pareto Diagram of evaluation grade

2 In order to determine the service life of the bulb , Randomly selected from a batch of bulbs 100 To test , The results obtained are shown in table 3-6 Shown .

surface 3-6　 Lamp life （ Company ： Hours ）
requirement ：.
（1） Based on the group distance 10 Group equally , Organize into frequency distribution table .
（2） Draw histogram according to grouped data , Explain the characteristics of data distribution .
（3） Make a stem and leaf map , And compare with histogram .

Explain ：（1） Compile frequency distribution table , As shown in the table 3-7 Shown .

surface 3-7　100 Frequency distribution of bulb service life
（3） Draw the histogram of bulb service life distribution , Pictured 3-3 Shown .

chart 3-3　 Histogram of lamp life distribution
（4） Construct the stem and leaf diagram of bulb service life distribution , Pictured 3-4 Shown .

chart 3-4　 Stem leaf diagram of bulb service life distribution
It can be seen from the histogram and stem leaf diagram of bulb service life distribution , The service life of bulbs is basically symmetrically distributed . The distribution characteristics reflected by histogram and stem leaf diagram are consistent , But the advantage of the stem and leaf map is to retain the information of the original data .

3 The utility model relates to a bagged food, which is automatically filled by a production line . The weight of each bag is about 50g, But for some reason , The weight of each bag will not be exactly 50g. Here is a random sample 100 Bag food , The measured weight data is shown in table 3-9 Shown .

surface 3-9　 Food weight （ Company ：g）

requirement ：
（1） Build the frequency distribution table of these data .
（2） Draw the histogram of frequency distribution .
（3） Explain the characteristics of data distribution .

answer ：（1） Construct the frequency distribution table of food weight , As shown in the table 3-10 Shown .

surface 3-10　 Frequency distribution table of food weight
（2） Draw the histogram of frequency distribution of food weight , Pictured 3-5 Shown .

chart 3-5　 Histogram of frequency distribution of food weight
（3） As can be seen from the histogram , The distribution of food weight is basically symmetrical .

4 Counter table 3-11 Plot a scatter plot of the data .

surface 3-11

Explain ： Draw a scatter plot , Pictured 3-6 Shown .

chart 3-6　 Scatter plot

5 nail 、 Class B and class B each have 40 Famous student , The distribution of final statistics test scores is shown in table 3-12 Shown .
surface 3-12　 The final statistics examination results of class A and class B

requirement ：
（1） According to the data above , Draw a bar chart and a ring chart comparing the exam results of the two classes .
（2） Compare the characteristics of the distribution of examination scores between the two classes .
（3） Draw a radar map , Compare whether the distribution of test scores of the two classes is similar .

Explain ：（1） Draw a comparison bar chart , Pictured 3-7 Shown .

chart 3-7　 Bar chart of final statistics examination results of class A and class B
Draw a circle , Pictured 3-8 Shown （ The inner ring is the result of class a ）.

chart 3-8　 Ring chart of final statistics examination results of class A and class B
（2） As can be seen from the bar chart , There are more people in class a who have achieved Intermediate Grades , The number of excellent and good is less , The number of people who fail is also higher than that of class B . Class B is different , There are more people with excellent and good exam results , The number of people below the middle level is less . This shows that the average score of class B is better than that of class a . This can also be clearly seen from the percentage of the ring chart .
（3） Draw a radar chart of the examination results of the two classes , Pictured 3-9 Shown .

chart 3-9　 Radar chart of final statistics examination results of class A and class B
It can be seen from the shape of the radar chart , There is no similarity between the examination results of the two classes .

6.1997 The average relative humidity data of several major cities in China in are shown in the table 3-13 Shown . Try to draw a box diagram , And analyze the distribution characteristics of the average relative humidity in each city .

surface 3-13　1997 The average relative humidity of several major cities in China in each month

Explain ： Draw the box diagram of the average relative humidity of each month in each city , Pictured 3-10 Shown .

 
chart 3-10　 Relative humidity box diagram of each city
It can be seen from the box diagram that , The monthly average relative humidity of each city is quite different . The cities with greater dispersion are mainly Beijing and Changchun （ The box is large ）; Chengdu is less dispersed 、 Guangzhou and Wuhan （ The box is small ）; Chengdu is the city with the largest relative humidity 、 Guangzhou 、 Nanjing and Wuhan （ The median is larger ）; The city with the lowest relative humidity is Lanzhou （ The median is small ）; The cities with symmetrical distribution of relative humidity are mainly Beijing 、 wuhan 、 Guangzhou and Lanzhou （ The median is roughly in the middle of the box , The maximum and minimum values are approximately the same distance from the box ）; Cities with asymmetric relative humidity mainly include Nanjing 、 Zhengzhou, etc ; The cities with extreme relative humidity are mainly Changchun and Xi'an .