InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What is statistical average? What desirable properties should an average possess? |
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Answer» Statistical average is the central value or the representative value of a statistical series. The following are some of the attributes of a good statistical average. It should be simple to calculate and understand It should be based on all the observations in the data It should be capable of further algebraic treatment It should not be affected by extreme values or by fluctuations in the sample |
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| 2. |
State four demerits of arithmetic mean. |
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Answer» 1. It cannot be located graphically. 2. A single item can bring big change in the result. For example if there are three terms 4, 7, 10 ; X is 7 in this case. If we add a new term 95, the new X is 4+7+10+95/4 = 116/4 = 29. This is a big change as compared to the size of first three terms’ X- . 3. Its value will be effective only if the frequency is normally distributed. Otherwise in case skewness is more, the results become ineffective. 4. In case of open end class intervals we have to assume the limits of such intervals and a little variation in X can take place. Such is not the case with median and mode, and there is no use of the open end intervals in its calculations. |
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| 3. |
Give the four objective of statistical average. |
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Answer» There are following four objectives of statistical average: (i) To present a brief picture of data : The main purpose of average is to present a simple and systematic description of the data. (ii) To represent the universe : It also helps to obtain a picture of a complete group. (iii) Basis of statistical analysis : It is the basis of statistical analysis as it analyse the data. (iv) To facilitate comparison : It helps in comparing the data of various categories. |
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| 4. |
State four merits of arithmetic mean. |
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Answer» 1. It can be easily calculated; and can be easily understood. It is the reason that it is the most used measure of central tendency. 2. As every item is taken in calculation, it is effected by every item. 3. As the mathematical formula is rigid one, therefore the result remains the same. 4. Fluctuations are minimum for this measure of central tendency when repeated samples are taken from one and the same population. |
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| 5. |
If the average salary of a firm is Rs. 400 and the number of workers is 60, find the total salary bill of the firm. |
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Answer» Given: `barX=400,N= 60` `barX=(sumX)/N` `rArr" "sumX= N xx barX` `" "=60xx400 = 24,000` Total Salary Bill = Rs. 24,000. |
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| 6. |
Mean of 100 observations is found to be 40. If at the time of computation two items are wrongly taken as 30 and 27 instead of 3 and 72, find the correct mean. |
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Answer» Given: `N = 100, barX = 40 ` `barX = (sumX)/N` Or,`" "40 = (sumX)/100` `:." "sumX("Wrong") = 40xx 100 = 4,000` Correct values = 3 + 72 = 75 Incorrect values = 30 + 27 = 57 `"Correct "barX=(sumX"(Wrong)+(Correct Value)-(Incorrect Value)")/N` ` = (4,000+75-57)/100=(4,018)/100=40.18` Corrected Mean = `40.18`. |
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| 7. |
Formula for finding arithmetic mean is:A. `barX = sum X`B. `barX = (sumX)/N`C. `barX = sum X-N`D. `barX = N/(sumX)` |
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Answer» Correct Answer - B It is the average of a set of numerical values, as calculated by adding them together and dividing by the number of terms in the set. |
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| 8. |
The average marks of 39 students of a class is 50. The marks obtained by 40th student are 39 more than the average marks of all the 40 student are 39 more than the average marks of all the 40 students. Find the mean marks of all the 40 students. |
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Answer» Let the mean marks of all the 40 students = `barX` Given: `barX_(1)=50,N_(1)= 39` Marks obtained by the 39 students `sum X =50 xx 39 = 1,950` Marks obtained by the 40th student `= barX+39` Mean marks of all the 40 students ` barX = (sumX)/N` `barX= (1,950+barX+39)/40 ` `40 barX = 1,989 + barX` `40 barX - barX = 1,989` `39 barX = 1,989` ` barX = (1,989)/39 = 51 ` Thus, Mean marks of all the 40 students = 51. |
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| 9. |
If a given number is subtracted from all the items in a series, then the arithmetic mean of that series will increase by the same specific value. |
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Answer» Correct Answer - false Then, the arithmetic mean of the series will decrease by the same specefic value. |
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| 10. |
Which of the following is a type of mathematical average?A. MedianB. Partition valueC. ModeD. None of these |
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Answer» Correct Answer - D In mathematics and statistics, average refers to the sum of a group of values divided by n, where n is the number of values in the group.none of these is the mathematical average. |
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| 11. |
Define and explain arithmetic mean. |
| Answer» The arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables. | |
| 12. |
Sum of deviations of different values from arithmetic mean is always equal to:A. zeroB. oneC. less than oneD. more then one |
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Answer» Correct Answer - A negative values will always cancel out the positive ones. |
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| 13. |
Define and explain weighted arithted arithmetic mean. |
| Answer» The weighted arithmetic mean equals the sum of observations multiplied by their weights divided by the sum of their weights. A weighted mean is a kind of average. Instead of each data point contributing equally to the final mean, some data points contribute more “weight” than others. | |
| 14. |
The mean of weighted items is called weighted average. |
| Answer» The mean of weighted items is called weighted average. | |
| 15. |
Which of the following is not a measure of central tendency?A. MeanB. ModeC. Standard deviationD. Median |
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Answer» Correct Answer - C Standard deviation is a quantity expressing by how much the members of a group differ from the mean value for the group.It is not a central tendency. |
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| 16. |
Discuss the various methods of measuring arithmetic mean and point out its merits and demerits. |
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Answer» (A) Merits: 1. It can be easily calculated; and can be easily understood. It is the reason that it is the most used measure of central tendency. 2. As every item is taken in calculation, it is effected by every item. 3. As the mathematical formula is rigid one, therefore the result remains the same. 4. Fluctuations are minimum for this measure of central tendency when repeated samples are taken from one and the same population. 5. It can further be subjected to algebraic treatment unlike other measures i.e. mode and median. 6. A.M. has also a plus point being a calculated quantity and is not based on position of terms in a series. 7. As it is rigidly defined, it is mostly used for comparing the various issues. (B) Demerits or Limitations: 1. It cannot be located graphically. 2. A single item can bring big change in the result. For example if there are three terms 4, 7, 10 ; X is 7 in this case. If we add a new term 95, the new X is 4+7+10+95/4 = 116/4 = 29. This is a big change as compared to the size of first three terms’ X- . 3. Its value will be effective only if the frequency is normally distributed. Otherwise in case skewness is more, the results become ineffective. 4. In case of open end class intervals we have to assume the limits of such intervals and a little variation in X can take place. Such is not the case with median and mode, and there is no use of the open end intervals in its calculations. 5. Qualitative forms such as Cleverness, Riches etc. cannot give X as data can’t be expressed numerically. 6. X cannot be located by inspection as in the case of mode and median. 7. Sometimes it gives impossible or laughable conclusions, e.g. if there are 60, 50 and 12 students in three classes then average number of students is 60+50+42/3 = 50.67, which is impossible as students can’t be in fractions. |
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| 17. |
In a class of 50 students 10 have failed and their average of marks is `2.5` . The total marks secured by the entire class were 281. Find the average marks those who have passed. |
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Answer» Given: N = 50, Failed Students = 10 Mean marks of those who failed = `2.5` Total marks secured by the entire class = 281 Total marks obtained by those who have passed = 281 - 25 = 256 Average marks obtained by those who have passed = `(256)/40 = 6.4` Average marks obtained by those who have passed = `6.4`. |
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| 18. |
Follwing are the marks obtained by 8 students in Statistics. Calculate the arithmetic mean. `{:("Marks",15,18,16,45,32,40,30,28):}` |
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Answer» `{:("Marks (X)"),(" "15),(" "18),(" "16),(" "45),(" "32),(" "40),(" "30),(" "28),(sumX=224):}` `barX=(sumX)/N=(X_(1)+X_(2)+...X_(10))/10=224/8=28` Average marks of the 8 students = 28. |
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| 19. |
Find the missing information in the following table: `{:(,,A,,B,,C,,"Combined"),("Number(N)",,10,,8,,-,," "24),("Mean"(barX),,20,,-,,6,," "15):}` |
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Answer» Missing number for C = 24 - (10+8) = 6 Let mean for B = x We know that, `barX_(123)=(barX_(1)N_(1)+barX_(2)N_(2)+barX_(3)N_(3))/(N_(1)+N_(2)+N_(3))` `:. " "15=((20xx10)+(8xxx)+(6xx6))/24` `200+8x+36=15 xx 24` `rArr" "236+8x=360` `rArr" "8x=360-236` `rArr" "8x=124` `rArr" "x=(124)/8` `rArr" "x = 15.5` Thus, Missing Number for C = 6. Mean of B = `15.5`. |
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| 20. |
Mean marks obtained by 100 students are estimated to be 40. Later on its is found that one value was read as 83 instead of 53. Find out the 'corrected' mean. |
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Answer» `barX=(sumX)/N` Or, `sumX=barXN` Given: `barX=40,N=100` `40=(sumX)/100` `:.sumX"(wrong)"=40xx100=4,000` Correct value = 53 Incorrect value=83 Correct `barX=(sumX"(Wrong)+(Correct value)-(Incorrect value)")/N` `=(4,000+53-83)/100` `=(3,970)/100=39.70` Thus, Corrected Mean = 39.70. |
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| 21. |
Indicate the most appropriate alternative from the multiple choices provided against each question. The algebraic sum of deviation of a set of n values from A.M. isA. nB. 0C. 1D. None of these |
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Answer» Correct Answer - b B |
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| 22. |
Indicate the most appropriate alternative from the multiple choices provided against each question. The most suitable average for qualitative measurement is:A. arithmetic meanB. medianC. modeD. N/A |
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Answer» Correct Answer - c C |
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