Statistics final examination paper

Simulated examination questions for the final exam of statistical principles

Panda Xie

Simulated examination questions for the final exam of statistical principles

Fill in the blanks (2 points for each small question, *** 10)

1. The symbol for unit attribute characteristics is _ _ _ _ _ _, and the symbol for unit quantity characteristics is _ _ _ _ _ _ _.

2. Any statistical distribution must meet the two conditions of _ _ _ _ _ _ _ and _ _ _ _ _ _.

3. Sampling estimation is to estimate the corresponding _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

4. In regression analysis, the dependent variable is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

5. There are _ _ _ _ _ _ _ _ _ and _ _ _ _ _ _ _ for calculating the total statistical indicators.

Second, true or false (2 points for each small question, *** 10)

1. Census is generally used to investigate the number of social and economic phenomena at a certain point in time, and it does not exclude the investigation of items belonging to the period phenomenon. ( )

2. In the same population, the value of the cycle index is directly proportional to the length of the cycle, and the value of the time index is inversely proportional to the time interval. ( )

3. In sampling inference, the sum index value is definite and unique, while the sample index value is a random variable. ( )

4. The characteristic of sampling score is that the greater the sampling score, the greater the sampling average error. ( )

5. In various dynamic series, the index value is restricted by the period reflected by the index. ( )

Iii. Multiple choice questions (2 points for each small question, *** 12 points)

1. The individual things that make up the statistical population are called ().

A. investigation unit B. marked value C. quality unit D. overall unit

2. The composite grouping is ()

A. Two or more populations are stacked and grouped with the same symbol.

B. choose a complex symbol for the group to be grouped.

C, overlapping and grouping two or more signs selected from the same crowd.

D. Select two or more signs of the same group and group them side by side.

3. The total index is divided into () according to the different time conditions.

A. Quantitative and qualitative indicators B. Time indicators and time indicators

C. Total unit amount and total mark amount D. Physical indicators and value indicators

4. The most commonly used method and the most basic form for calculating the average index is ().

A. Number of central defenders B. Mode C. Arithmetic average D. Harmonic average

5. According to the different properties of indexation indicators, statistical indicators can be divided into ().

A. Total indicators and individual indicators B. Quantitative indicators and quality indicators

C. Average index and average index D. Composite index and average index

6. When calculating the chronological average, the "half method" is applicable to ()

A. periodic series calculates the average value arranged in time sequence. Equal-interval time series calculates the average in chronological order.

C, calculating the time sequence average value of time series with unequal intervals D, calculating the time sequence average value of relative time series dynamic series composed of two time series.

Four, multiple-choice questions (2 points for each small question, ***8 points)

1. Digital distribution sequence ()

A it consists of two factors: the group divided into a whole by a symbol and the number of units in each group.

B it consists of group distance and group number, group limit and group median.

C, including mass distribution series and variable series.

D. it can be expressed in the form of charts.

E. can prove the overall structure and distribution characteristics.

2. The investigation unit is ()

A. Population to be investigated

B. the person in charge of the whole unit that needs to be investigated

C. investigate the undertaker of the project

D. Unit responsible for reporting findings

E. Specific units included in the survey.

3. Sampling error in sampling estimation ()

A. it is inevitable.

B can be eliminated by improving the investigation method.

C. it can be calculated in advance.

D. it can only be calculated after the investigation is completed.

E. its size can be controlled.

4. Let the linear regression equation from product unit cost (yuan) to output (100 pieces) be yc=76- 1.85x, that is, ().

A For every 100 pieces produced, the average unit cost will be reduced by 1.85 yuan.

B For every 100 pieces produced, the average unit cost will be reduced by 1.85 yuan.

C. output and unit cost change in opposite directions.

D. the output and unit cost change in the same direction.

E when the output is 200 pieces, the unit cost is 72.3 yuan.

Verb (abbreviation of verb) question and answer (5 points for each small question, *** 10)

1. Briefly describe the concept and function of variation index.

2. What is the basic meaning and computer form of the average index?

Six, calculation problems (each small 10 points, ***50 points)

1. The scores (scores) of 40 students in a class are:

57 89 49 84 86 87 75 73 72 68 75 82 97 8 1

67 8 1 54 79 87 95 76 7 1 60 90 65 76 72 70

86 85 89 89 64 57 83 8 1 78 87 72 6 1

According to the regulations of the school, a score below 60 means failing, a score of 60-70 means passing, a score of 70-80 means being average, a score of 80-90 means being good, and a score of 90- 100.

Out of kindness. Requirements:

(1) Divide the students in this class into five groups: failing, passing, average, good and excellent, and draw up a frequency distribution table.

(2) indicate the grouping mark and type; Analyze the exam situation of the students in this class.

2. The output of three workshops in a factory in the first quarter is as follows:

Workshop Planned Completion Percentage Actual Output (Pieces) Unit Product Cost (Yuan \ Pieces)

90% of the first workshop19815

The second workshop 105% 3 15 10

The third workshop 1 10% 220 8

According to the above data:

(1) Average planned completion percentage of output of three workshops in the first quarter.

(2) The average unit product cost of the three workshops in the first quarter.

3. Through regression analysis, the linear regression equation between the yield per mu (Y, unit "Mu Dan") and the watering amount (X, unit "inch") of a certain crop is YC = 2.82+1.56x. It is also known that the variance of variable X is 99.75 and that of variable Y is 3 12.82.

Requirements: (1) Calculate the yield per mu when the watering amount is 0;

(2) Calculate the average yield per mu for every inch of watering;

(3) Calculate the correlation number between watering amount and yield per mu, and analyze the correlation degree and direction.

(Formula and calculation program are required, and the result is reserved to two decimal places. )

4. The unit cost of an enterprise's products is 1988, which is 2% lower than 1987, 5% lower than 1989, 3% lower than 1996554. Based on 1987, the total and average decline rates of the unit cost of this enterprise from 1988 to 199 1 are calculated. (It is required to write out the formula and calculation process, and the result shall be kept at four decimal places. )

200 pieces were selected from a batch of parts for testing, of which 188 pieces were qualified.

Requirements: (1) Calculate the sampling average error of the qualified rate of this batch of parts;

(2) According to the reliability of 95.45% (t=2), estimate the qualified rate of this batch of parts at intervals.

6. The unit cost of an enterprise's products is 1988, which is 2% lower than 1987, 5% lower than 1989, 3% lower than 1996554. Based on 1987, the total and average decline rates of the unit cost of this enterprise from 1988 to 199 1 are calculated. (It is required to write out the formula and calculation process, and the result shall be kept at four decimal places. )

7. 200 pieces were selected from a batch of parts for testing, of which 188 pieces were qualified.

Requirements: (1) Calculate the sampling average error of the qualified rate of this batch of parts;

(2) According to the reliability of 95.45% (t=2), estimate the qualified rate of this batch of parts at intervals.

Final Examination Paper of Statistics Course of Beijing Information Science and Technology University (Volume A)

Beijing Information Science and Technology University

The first semester of the 2007-2008 school year

College where the course is located: School of Economics and Management, applicable professional course: Note: 050 1502.

Examination form: (closed book)

First, multiple-choice questions (this topic is entitled * * 15, and each topic is 1 point, * *1point)

Of the four options listed in each question, only one meets the requirements of the topic. Please fill in the code in brackets after the title. Wrong selection, multiple selection or no selection will not be scored.

1. Which of the following does not belong to the basic assumption (D) in unary regression?

A. for all x, the variance of the error term is the same.

B. the error term obeys the normal distribution.

C. the error terms are independent of each other

2. When the skewness coefficient of a group of data distribution is negative, the relationship among the mode, median and mean of the data is (a).

A. most >; Median > mean/mean

B. average value >; Median > mode

C. median >; Most >; Mean value/mean value

D. median >; Average > mode

3. The univariate regression equation is y = 1 1.64-0.25x, then the following statement is correct (c).

A. The independent variable increased by 1 unit on average, and the dependent variable decreased by 0.25 unit on average.

B. there is a positive correlation between independent variables and dependent variables.

4. If there are two series A and B, then the average of series (A) is very representative.

A. 1 < 2 1 > 2, the average value of series b is highly representative.

B. 1 < 2 1 > 2, the average of series b is less representative.

C. 1 = 2 1 > 2, the representation of the average value of the sequence a is high.

D. 1 = 2 1 < 2, and the average value of series A is less representative.

5. If the last group of the continuous variable sequence is an open group, the lower limit is 500, and the group median of the adjacent group is 480, then the group median of the last group is (a).

520 B.5 10 C.500 D.540

6. The average value unaffected by extreme variable values is (d).

A. Arithmetic average B. Harmonic average

C. geometric average D. mode

7. There are 20 workers to look after the machine, the number is as follows: 2, 5, 4, 4, 3, 4, 2, 2, 4, 3, 4, 6, 3, 4, 5, 2, 4. If the frequency distribution series is compiled according to the above data, the method (a) should be adopted.

A. single grouping B. equidistant grouping C. unequal grouping D. any of the above groupings is acceptable.

8. If there is no seasonal change, the seasonal ratio should be (b).

A.0b. 1 c. greater than1d. less than1

9. If a qualitative variable has m categories, it is necessary to introduce (c) dummy variables.

Morning and afternoon+1

C.m-1d. can't judge.

10. The average length of service of workers in the first group is 5 years, that in the second group is 7 years, and that in the third group is 10 years. The number of workers in the first group accounts for 20% of the total, and the second group accounts for 60%, so the average length of service of the three groups of workers is (b).

A.8 years B.7.2 years C.5 years D.7.8 years

1 1. The output of various products of an enterprise in 2007 increased by 8% compared with that in 2006, and the total production cost increased by 12%, so the unit cost of the factory in 2007 was (d).

A. decreased by 0.62%; B. an increase of 0.62%.

C. It decreased by 3.7%, while D. It increased by 3.7%.

12. Sign of correlation coefficient r and slope b2 (A).

A. Same B. Different

C. unable to judge

13. It is known that the comprehensive price index of the two stocks bought by Xiao Jiang rose by 24 points. The average closing price of the stock today was 14 yuan, and the average closing price the day before yesterday was (c).

10.64

C.11.29d. cannot be calculated.

14. If this year's growth rate is 1 12% compared with last year, and last year's growth rate is 3% compared with the year before, then this year's average growth rate is (d).

A.9.0% B.7.4%

C.7.5% D. 15.4%

15. It is known that the absolute increase of 1% this year is 0.54, and the absolute increase last year is 5, so the growth rate last year is (c).

9.3% and 8.7%

C.10.2% D. cannot be calculated.

Second, multiple-choice questions (2 points for each small question, *** 16 points)

Each question lists several options that meet the requirements of the topic. Please put the letter before the correct option in brackets after the topic. Multiple choices, fewer choices, and wrong choices all have no scores.

1. The following variables are discrete variables.

A. Quantity of products in stock B. Ratio of current assets to current liabilities

C. Total weight of goods D. Quantity of goods measured by individuals

E. Traffic volume of toll roads F. Attending the annual meeting of the company

2. It is pointed out that the following data collection belongs to the method of collecting data through experiments (A B E).

A comparison between the new method and the traditional method of training air ticket agents

Compare the two assembly instructions by asking two groups of comparable children to assemble toys with two different assembly instructions.

A product evaluation magazine mailed a questionnaire to its subscribers, asking them to rank their recently purchased products.

Interview customers in the shopping center and ask them why they shop there.

E Compare two different pension promotion methods by adopting different methods in two comparable regions.

3. Which of the following statements about group limit is correct (A B D).

A. According to the number of employees, the group boundaries of adjacent groups may overlap or be discontinuous.

B employees are grouped by salary, and their group limits must overlap.

C. students are grouped according to their grades, and the grouping restrictions must be interrupted.

D. People are grouped according to their height, and their grouping boundaries must overlap.

4. The following belong to the quality index (A B D E).

A. Price index B. Unit cost index

C. Sales volume index D. Wage level index

E. labor productivity index

5. Specifically, if the following (A B C) occurs, it means that multiple * * * linearities may exist in multiple regression models.

A. There is a significant correlation between pairs of independent variables in the model.

B. the linear relationship is significant, but the t test of regression coefficient is not significant.

C. the sign of the regression coefficient is contrary to the expectation.

6. Which of the following properties does the arithmetic mean have (B C)?

A.(x-) = minimum B. (x-) = 0

C.(x-) 2 = minimum D. (x-) 2 = 0

E.(X- )= 1

7. In the frequency distribution series.

A. The total number of times is fixed, and the frequency is inversely proportional to the frequency. B the sum of each group of frequencies is equal to 100.

C. Each group of frequencies is greater than 0, and the sum of frequencies is equal to1d. The smaller the frequency, the smaller the effect of this group of values.

E frequency indicates the relative influence of each group of variable values on the population.

8. Standard deviation.

A. the general level indicating the mark value of the overall unit B. the general level reflecting the overall unit

C. Reflect the dispersion degree of the overall unit mark value D. Reflect the concentration trend of the overall distribution

E. reflect the overall distribution trend.

Three, short answer questions (this big question ***2 questions, each question 5 points, *** 10 points)

1. What is the annualized growth rate? What's the use?

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

(1) can be divided into single variable value grouping and group spacing grouping.

Single variable value grouping: take one variable value as a group; Suitable for discrete variables; It is suitable for cases with few variable values (+1).

Group spacing grouping: take the interval of a variable value as a group; Suitable for continuous variables; It is suitable for cases with many variable values; Need to follow the principle of "no weight and no leakage"; Equal length packets or unequal length packets can be used. (+ 1)

(2) A. Determine the number of groups:

(+ 1)

B Determine the group distance: the class width is the difference between the upper and lower limits of a group, which can be determined according to the maximum and minimum values of all data and the number of groups divided (+1).

C count the frequencies of each group and arrange them into a frequency distribution table. (+ 1)

Four. True or false (this big question is ***5 small questions, each small question is 1 point, and there are ***5 points)

1. When the correlation coefficient is+1, the two variables are completely correlated, and when the correlation coefficient is-1, the two variables are irrelevant. (error)

2. If the prices of various commodities increase by 5% on average and the sales volume decreases by 5% on average, the sales index will remain unchanged. (error)

3. When continuous variables and discrete variables are grouped by group spacing, the group limit can be determined by overlapping the group spacing of adjacent groups. (right)

4. According to the established linear regression equation, we can't judge the closeness of the correlation between two variables. (right)

5. Let p stand for unit cost and q stand for output, then ∑ p1q1-∑ p0q1stands for the influence of product unit cost change on total output. (error)

Four, the calculation analysis problem (***54 points)

1. Approximate the weight of outbound parcel samples in the post office to ounces: 2 1,18,30, 12, 14,17,28, 10. Calculate the mean, median, mode, range and quartile interval of this group of data, and describe the distribution pattern of data from the perspective of skewness (10).

2. Table 1 lists the sample data of students' extracurricular study time in the three-week business statistics course and their test scores at the end of the course as follows:

Table 1 Statistics of students' extracurricular study time and test scores

Student sample 1 2 3 4 5 6 7 8

Study time, x 2016 34 23 27 3218 22

Test score, Y 64 6 1 84 70 88 92 72 77

Regression with EXCEL, the result is as follows: (* *15)

Summary output

Regression statistics

Multiply R 0.862 109

R squared 0.74232

The adjusted r square is 0.700437.

Standard error 6. 157605

Observation value 8

Variance analysis

Significance f

Regression analysis+0 650.10080.000000000005

The remaining 6 227.4966 37.438+0 1

A total of 7,886 people.

Coefficient standard error t statistical p value

Intercept 40.08163265 8.8895514.50884785 0.0065471

Variable x11.496598639 0.359194.167419150.0058995954

Analyze and answer the following questions:

(1) What is the correlation coefficient between study time and test scores, and how much of the deterioration of test scores is caused by the change of study time? 86.2 1% 74.32%

(2) According to the result of EXCEL regression output, write the estimated regression equation, and explain the practical significance of regression coefficient.

(3) Test the significance of the linear relationship.

(4) According to the standardized residual diagram, it is judged whether the hypothesis about the normal distribution of random error terms is established.

The standardized residual distribution is between -2 and 2, so the assumption that the random error term obeys the normal distribution holds.

3. Randomly select the relevant data (unit: yuan) of similar products sold in 15 large shopping malls, and use EXCEL to regression the results. The following table shows the results: (* *15).

Summary output

Regression statistics

Multiply R 0.593684

R squared 0.35246

The adjusted r square is 0.244537.

The standard error is 69.75 12 1

Observed value 15

Variance analysis

Significance f

Regression analysis 231778.6438+05155909.00000000005

Remaining 12 58382.78 4865.232

Total 14 90 160.93

Coefficient standard error t statistical p value

Intercept 375.6018288 339.4105621.10662976 0.290145025.

X variable10.5378409510.21044674 2.5571054 0.02519961

X variable 21.457193542 0.667706586 2.18238606 0.049681066.

Correlation coefficient matrix

Y X 1 X2

Y 1

X 1 0.308952067 1

X2 0.00 12 14062 0.8528576 1

Note: the variable x 1 is the purchase price/yuan.

X variable 2 is sales expense/yuan.

Dependent variable y is sales price/yuan.

(1) indicates the correlation coefficient between y and X 1 and between y and X2. Is there any evidence that there is a linear relationship among purchase price, sale price and sales expenses? 0.3089 0.00 12 not, because the correlation coefficient is small.

(2) According to the results of the complaint, do you think it is useful to forecast the purchase price and sales expenses? invalid

(3) According to the results of EXCEL regression output, write the estimated regression equation to test whether the linear relationship is significant (). Not significant

(4) Explain the determining coefficient R2. Is the conclusion consistent with question (2)? R2=35.25%。 In the total variation of sales price, the proportion explained by estimated regression equation is 35.25%, which is consistent with each other. (+3)

(5) What is the correlation coefficient between x1and X2? What does this mean? Highly correlated

(6) Is there multiple * * * linearity in the model? Any special suggestions for the model? There may be multiple * * * linearities; Further test whether there is multiple * * * linearity, and test the significance of the sample correlation coefficient of X 1 X2 (rx 1x2=-0.8529). If it is significant, it can be determined that there is multiple * * * linearity. (+2)

Suggestions for the model: according to the research purpose, delete the relatively minor explanatory variables. (+ 1)

4. The data of the following three products produced by a company are shown in the following table (*** 14):

Unit price of commodity measures unit sales volume (ten thousand yuan)

2005, 2006, 2005, 2006

One kilogram 400 480 0.8 0.82

B ton 80881.151.05

Part c 50 60 1.20 1.38

(1) Calculate the sales index of three products;

(2) calculating the sales indices of the three products;

(3) calculating the unit price index of the three products;

(4) Calculate and analyze the relative number and absolute number of the influence of output and unit price changes on sales.

Beijing Information Science and Technology University

The first semester of the 2007-2008 school year

Standard Answers to Statistics Final Exam Paper (Volume A)

First, multiple-choice questions (this topic is entitled * * 15, and each topic is 1 point, * *1point)

1. (1) 2. (1) 3. (C) 4。 (A) 5。 (4)

6. Article 7, paragraph 1, paragraph 8, paragraph 2, paragraph 9. (C) 10。 (2)

1 1. 12。 (A) 13。 (C) 14。 15。 (3)

Second, multiple-choice questions (2 points for each small question, *** 16 points)

Of the five options listed in each question, two to five meet the requirements of the topic. Please put the letter before the correct option in brackets after the topic. Multiple choices, fewer choices, and wrong choices all have no scores.

1.(ADEF)。 (Abe) 3. (ABD ) 4。 (Abdul) 5. (ABC)

6. Seven years (BC). (CDE)。 (CE)

Three, short answer questions (this big question ***2 questions, each question 5 points, *** 10 points)

1. What is the annualized growth rate? What's the use?

(1) When the growth rate is expressed in years, it is called annualized growth rate or annual rate, (+2)

Its calculation formula is:

M is the number of cycles in a year; N is the total number of spans.

When the quarterly growth rate is annualized, m = 4.

When the monthly growth rate is annualized, m = 12.

When m = n, the above formula is the annual growth rate (+2).

(2) Monthly growth rate or quarterly growth rate can be converted into annual growth rate to achieve comparability between growth rates. (+ 1)

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

(1) can be divided into single variable value grouping and group spacing grouping.

Single variable value grouping: take one variable value as a group; Suitable for discrete variables; It is suitable for cases with few variable values (+1).

(2) A. Determine the number of groups:

(+ 1)

C count the frequencies of each group and arrange them into a frequency distribution table. (+ 1)

Four. True or false (this big question is ***5 small questions, each small question is 1 point, and there are ***5 points)

1. When the correlation coefficient is+1, the two variables are completely correlated, and when the correlation coefficient is-1, the two variables are irrelevant. (×)

2. If the prices of various commodities increase by 5% on average and the sales volume decreases by 5% on average, the sales index will remain unchanged. (×)

3. When continuous variables and discrete variables are grouped by group spacing, the group limit can be determined by overlapping the group spacing of adjacent groups. (√)

4. According to the established linear regression equation, we can't judge the closeness of the correlation between two variables. (√)

5. Let p stand for unit cost and q stand for output, then ∑ p1q1-∑ p0q1stands for the influence of product unit cost change on total output. (×)

Verb (abbreviation of verb) calculation and analysis (***55 points)

Median position: (10+ 1)/2=5.5.

median

Describe the distribution pattern of data from the perspective of skewness: mean > median, positive (right) skewness.

(+2)

2.( 1) What is the correlation coefficient between study time and test scores, and how much of the deterioration of test scores is caused by the change of study time?

r=0.862 109，(+ 1)

R2=0.743232, and 74.3232% of the deterioration of test scores is caused by the change of study time. (+2)

(2) According to the result of EXCEL regression output, write the estimated regression equation, and explain the practical significance of regression coefficient.

(+3)

The regression coefficient means that the average test score increases by 1.497 for every hour of study time. (+2)

(3) test the significance of linear relationship

Significant F = 0.005895457÷5%

Linear relationships are important. (+3)

(4) Judging whether the assumption that the random error term obeys the normal distribution is established according to the standardized residual diagram.

The standardized residual distribution is between -2 and 2, so the assumption that the random error term obeys the normal distribution holds. (+4)

(1) indicates the correlation coefficient between y and X 1 and between y and X2. Is there any evidence that there is a linear relationship among purchase price, sale price and sales expenses?

( 1)ryxi = 0.308952067 ry x2 = 0.00 12 14062，

There is no evidence. (+2)

(2) According to the above results, do you think it is useful to use purchase price and sales expenses to forecast?

Useless (+2)

(3) According to the results of EXCEL regression output, write the estimated regression equation to test whether the linear relationship is significant ().

Significant F = 0.073722 & gt=5%

The linear relationship is not significant. (+3)

(4) Explain the determining coefficient R2 to see if the conclusion is consistent with the question (2).

R2=35.25%。 In the total variation of sales price, the proportion explained by estimated regression equation is 35.25%, which is consistent with each other. (+3)

(5) What is the correlation coefficient between x1and X2? What does this mean?

Rx 1x2=-0.8529, highly correlated (+2).

(6) Is there multiple * * * linearity in the model? Any special suggestions for the model?

There may be multiple * * * linearities; Further test whether there is multiple * * * linearity, and test the significance of the sample correlation coefficient of X 1 X2 (rx 1x2=-0.8529). If it is significant, it can be determined that there is multiple * * * linearity. (+2)

Suggestions for the model: according to the research purpose, delete the relatively minor explanatory variables. (+ 1)

4.( 1) sales index of three products; (+3)

Sales indices of the three products = ∑ q1p1∑ q0p0.

=568.8/472= 120.5 1%

∑ q1p1-∑ q0p0 = = 568.8-472 = 968,000 yuan.

(2) the sales targets of the three products; (+3)

Iq=∑q 1p0 1/∑q0p0

=557.2/472= 1 18.05%

∑q 1p0-∑q0p0

= 557.2-472 = 852,000 yuan

(3) Price indices of the three products; (+3)

IP =∑q 1p 1/∑q 1p 0