statistics, 20 mcqs for tgt exam with explained answers
Here are 20 multiple choice questions (MCQs) on statistics for TGT exam preparation, each with an explained answer for better understanding[1][4][5][6][7]:
### MCQ Questions and Answers
1. **The mean of 2, 4, 6, 8, 10 is:**
- a) 4
- b) 5
- c) 6
- d) 8
**Answer:** c) 6. Mean is calculated as $$\frac{2+4+6+8+10}{5} = 6$$ [1].
2. **Which measure divides a distribution into two equal halves?**
- a) Mean
- b) Median
- c) Mode
- d) Range
**Answer:** b) Median. Median is the middle value that divides the dataset into two equal parts[1].
3. **If the most frequent value in a dataset is 8, what is this value called?**
- a) Mean
- b) Median
- c) Mode
- d) Range
**Answer:** c) Mode. Mode is the value that appears most frequently[1].
4. **Which measure of dispersion is most influenced by extreme values?**
- a) Range
- b) Mean deviation
- c) Standard deviation
- d) Quartile deviation
**Answer:** a) Range. Range is calculated from the extreme values (maximum - minimum)[1].
5. **If mean and mode of a data set are 12 and 16 respectively, what is the median?**
- a) 10
- b) 12
- c) 14
- d) 16
**Answer:** c) 14. Using the formula Mode = 3(Median) - 2(Mean), 16 = 3(Median) - 24 → Median = 14[1].
6. **For grouped data, frequencies are assumed to be:**
- a) Centred at the class marks
- b) Centred at the upper limits
- c) Evenly distributed over all classes
- d) Centred at lower limits
**Answer:** a) Centred at the class marks; it simplifies mean calculation for grouped data[5].
7. **The middlemost value in an odd numbered dataset is:**
- a) Mean
- b) Median
- c) Mode
- d) Range
**Answer:** b) Median. Median is the middle value in an ordered dataset[1].
8. **The formula for calculating mean of grouped data is:**
- a) $$\frac{\sum fi}{\sum xi}$$
- b) $$\frac{\sum fi xi}{\sum fi}$$
- c) $$\frac{\sum xi}{n}$$
- d) $$\frac{\sum fi^2}{n}$$
**Answer:** b) $$\frac{\sum fi xi}{\sum fi}$$. This is the weighted mean formula for grouped data[1].
9. **The cumulative frequency of a class is:**
- a) Average frequency
- b) Class mark
- c) Class height
- d) Sum of frequencies before and including that class
**Answer:** d) Sum of frequencies before and including that class; it's important for median calculation[5].
10. **The coefficient of variation (CV) is calculated as:**
- a) $$\frac{\text{Mean}}{\text{Standard deviation}} \times 100$$
- b) $$\frac{\text{Standard deviation}}{\text{Mean}} \times 100$$
- c) $$\frac{\text{Median}}{\text{Mode}} \times 100$$
- d) $$\frac{\text{Range}}{\text{Mean}} \times 100$$
**Answer:** b) $$\frac{\text{Standard deviation}}{\text{Mean}} \times 100$$; CV compares spread relative to mean[6].
11. **The interquartile range (IQR) measures:**
- a) The spread between minimum and maximum values
- b) The spread of middle 50% values
- c) The spread between mean and mode
- d) The spread of all values
**Answer:** b) The spread of middle 50% values; IQR = $$Q_3 - Q_1$$[6].
12. **A dataset: . What is the median?**
- a) 15
- b) 17
- c) 19
- d) 21
**Answer:** b) 17. Median is the middle value in the ordered dataset[1][4].
13. **The standard deviation of 0, 1, 2, ..., 9 is K. What is the standard deviation of 10, 11, ..., 19?**
- a) K
- b) K+10
- c) K*10
- d) K/10
**Answer:** a) K; shifting all values by a constant does not change standard deviation[1].
14. **If the sum of data is 60 and number of observations is 12, mean is:**
- a) 5
- b) 10
- c) 12
- d) 15
**Answer:** a) 5. Mean = 60 ÷ 12 = 5[1].
15. **What is the modal class in a frequency table?**
- a) Class with largest frequency
- b) Class with smallest frequency
- c) First class
- d) Last class
**Answer:** a) Class with largest frequency[5].
16. **Which method is most commonly used to calculate mean of large grouped data?**
- a) Direct method
- b) Assumed mean method
- c) Step deviation method
- d) All of these
**Answer:** d) All of these can be used depending on convenience[5].
17. **Numerical methods and graphical methods are categorized under:**
- a) Social statistics
- b) Business statistics
- c) Descriptive statistics
- d) Education statistics
**Answer:** c) Descriptive statistics; they deal with data representation[7].
18. **Which is not a measure of central tendency?**
- a) Mean
- b) Mode
- c) Median
- d) Standard deviation
**Answer:** d) Standard deviation; it measures dispersion, not central tendency[5].
19. **Sampling techniques are used in statistics for:**
- a) Data collection
- b) Data analysis
- c) Data representation
- d) Data interpretation
**Answer:** a) Data collection; sampling is a process to collect representative data[3].
20. **The mean of x, x+2, x+4, x+6, x+8 is 12. What is x?**
- a) 4
- b) 6
- c) 8
- d) 10
**Answer:** b) 6. Mean: $$\frac{x+x+2+x+4+x+6+x+8}{5}=12$$, solve: $$5x+20=60$$, $$x=8$$ [Correction: d) 8][2].
***
20 more
Here are 20 more MCQs on statistics for TGT exam preparation with explained answers:
1. **The sum of deviations of all observations from the mean is always:**
a) Zero
b) Positive
c) Negative
d) Equal to mean
**Answer:** a) Zero. By definition, deviations around the mean sum to zero[3].
2. **The measure which is not influenced by extreme values is:**
a) Mean
b) Median
c) Mode
d) Range
**Answer:** b) Median. Median is resistant to outliers[7].
3. **Variance is measured in:**
a) Original units
b) Square of original units
c) Cube of original units
d) Same as standard deviation
**Answer:** b) Square of original units. Variance is square of deviations[2].
4. **The probability of an impossible event is:**
a) 1
b) 0
c) 0.5
d) Depends on event
**Answer:** b) 0. Impossible event has zero probability[5].
5. **If the mean is 75 and the standard deviation is 5, the coefficient of variation is:**
a) 7.5%
b) 6.6%
c) 15%
d) 5%
**Answer:** a) 6.67%. CV = (SD/Mean)*100 = (5/75)*100 = 6.67%[11].
6. **If a dataset is perfectly symmetrical, then the skewness is:**
a) Positive
b) Negative
c) Zero
d) Undefined
**Answer:** c) Zero. Symmetrical distribution has zero skewness[7].
7. **In a frequency distribution, the class midpoint is:**
a) Sum of class limits
b) Average of class limits
c) Difference between class limits
d) Twice the class limits
**Answer:** b) Average of class limits[3].
8. **The mode of the data 1, 3, 3, 5, 7, 7, 7, 8, 9 is:**
a) 3
b) 7
c) 5
d) 8
**Answer:** b) 7, as it appears most frequently[2].
9. **If all values in a dataset increase by 5, the mean:**
a) Increases by 5
b) Remains same
c) Decreases by 5
d) Doubles
**Answer:** a) Increases by 5[2].
10. **The median location for an even number of observations is:**
a) Middle observation
b) Average of two middle observations
c) Lowest observation
d) Highest observation
**Answer:** b) Average of two middle observations[7].
11. **If mean = median > mode, the distribution is:**
a) Positively skewed
b) Negatively skewed
c) Symmetrical
d) Uniform
**Answer:** a) Positively skewed[7].
12. **Chi-square test is used for testing:**
a) Difference of means
b) Association between categorical variables
c) Variance equality
d) Correlation
**Answer:** b) Association between categorical variables[1].
13. **Hypothesis testing helps in:**
a) Describing data
b) Drawing conclusions about a population
c) Calculating probabilities
d) Organizing data
**Answer:** b) Drawing conclusions about a population from sample[1].
14. **A sample drawn without replacement is:**
a) Simple random sampling
b) Systematic sampling
c) Stratified sampling
d) Cluster sampling
**Answer:** a) Simple random sampling[1].
15. **Standard deviation is:**
a) Average deviation
b) Square root of variance
c) Sum of deviations
d) None of these
**Answer:** b) Square root of variance[2].
16. **In a normal distribution, the mean, median, and mode:**
a) Are equal
b) Are different
c) Mean > median > mode
d) Mode > median > mean
**Answer:** a) Are equal[7].
17. **The range of data helps to:**
a) Measure central tendency
b) Measure dispersion
c) Calculate variance
d) Calculate mean
**Answer:** b) Measure dispersion[2].
18. **When the correlation coefficient is zero it means:**
a) No relationship between variables
b) Perfect positive correlation
c) Perfect negative correlation
d) None of these
**Answer:** a) No linear relationship between variables[2].
19. **The upper quartile (Q3) represents:**
a) 25% of data below it
b) 50% of data below it
c) 75% of data below it
d) 100% of data below it
**Answer:** c) 75% of data below it[11].
20. **The range of the numbers 2, 5, 7, 8, 10 is:**
a) 8
b) 5
c) 10
d) 2
**Answer:** a) 8. Range = maximum - minimum = 10 - 2[2].
20 more
Here are 20 more multiple choice questions (MCQs) on statistics for TGT exam preparation with explained answers, drawn from current educational resources and tailored for comprehensive coverage:
1. The range of the observations 2, 4, 7, 11, 15 is:
a) 7
b) 11
c) 13
d) 15
**Answer:** c) 13. Range = Maximum - Minimum = 15 - 2 = 13 [1].
2. The median of the data set 3, 8, 9, 15, 17 is:
a) 8
b) 9
c) 10
d) 15
**Answer:** b) 9. Median is the middle value in an ordered set [1].
3. In a symmetrical distribution, mean, median, and mode are:
a) All different
b) Mean = Median > Mode
c) Mean < Median < Mode
d) Equal
**Answer:** d) Equal [7].
4. If the mean of 10 numbers is 20 and one number is excluded, the mean of remaining is 18. What is the excluded number?
a) 30
b) 22
c) 24
d) 28
**Answer:** a) 30. Total sum = 200, sum of 9 numbers = 18 × 9 = 162, excluded number = 200 - 162 = 38 [2].
5. The formula for variance (𝜎²) is:
a) Mean of squares - square of mean
b) Square of mean - mean of squares
c) Mean of deviations
d) Sum of deviations
**Answer:** a) Mean of squares - square of mean [1].
6. The probability of an event that is certain to occur is:
a) 1
b) 0
c) 0.5
d) Depends on situation
**Answer:** a) 1 [5].
7. The standard deviation of the data set 5, 5, 5, 5 is:
a) 0
b) 5
c) 10
d) 20
**Answer:** a) 0. No variation among values [3].
8. If the size of sample increases, standard error:
a) Increases
b) Decreases
c) Remains same
d) None of these
**Answer:** b) Decreases [5].
9. Which of the following is not a sampling method?
a) Random sampling
b) Stratified sampling
c) Non-probability sampling
d) Parametric sampling
**Answer:** d) Parametric sampling [2].
10. Mode can be used for data measured on:
a) Nominal scale
b) Ordinal scale
c) Interval scale
d) Ratio scale
**Answer:** a) Nominal scale [1].
11. The correlation coefficient varies between:
a) 0 and 1
b) -1 and 1
c) 0 and 100
d) None of these
**Answer:** b) -1 and 1 [1].
12. The sum of probabilities of all mutually exclusive outcomes of an experiment must be:
a) 0
b) 0.5
c) 1
d) 2
**Answer:** c) 1 [5].
13. The mean deviation is:
a) Mean of absolute deviations from the mean
b) Mean of squared deviations from the mean
c) Median of deviations
d) Mode of deviations
**Answer:** a) Mean of absolute deviations from the mean [3].
14. In hypothesis testing, the significance level is the probability of:
a) Type I error
b) Type II error
c) Correct decision
d) None of these
**Answer:** a) Type I error [2].
15. A positive skewed distribution has:
a) Mode > Median > Mean
b) Mean > Median > Mode
c) Median > Mean > Mode
d) Mean = Median = Mode
**Answer:** b) Mean > Median > Mode [7].
16. Which distribution is known as "bell-shaped"?
a) Poisson distribution
b) Binomial distribution
c) Normal distribution
d) Exponential distribution
**Answer:** c) Normal distribution [7].
17. The mode of grouped data lies:
a) At highest frequency class
b) Between median and mean
c) At average of frequencies
d) None of these
**Answer:** a) At highest frequency class [1].
18. In an experiment, total number of outcomes is 36. Probability of an event happening is 1/6. Number of favorable outcomes is:
a) 5
b) 6
c) 7
d) 12
**Answer:** b) 6 [5].
19. If events A and B are independent, then:
a) P(A and B) = P(A) + P(B)
b) P(A or B) = P(A) + P(B) - P(A and B)
c) P(A and B) = P(A) × P(B)
d) P(A or B) = 1
**Answer:** c) P(A and B) = P(A) × P(B) [5].
20. The sum of squared deviations from the mean is always:
a) Zero
b) Positive
c) Negative
d) Depends on data
**Answer:** b) Positive. Sum of squared deviations cannot be negative [1].
