For the price -quantity chart
the Laspeyres price index for current year is
SSC CGL Tier-2 10th August 2022 Statistics
For the following questions answer them individually
For completely randomised design for k treatments and n observations, $$y_{if}$$ = response from the $$j^{th}$$ unit receiving $$i^{th}$$ treatment, $$\sum_i \sum_j y_{ij} = y_{..}$$ and $$\sum_j^{ni} y_{ij} = y_{i.}$$. Which of the following options is correct?
Two data set of size 9 and 6 have standard deviation 3 and 4 respectively and arithmetic means 3 and 3 respectively. The standard deviation of combined data set of size 15 is
For the variables X, Y and Z, $$r_{XY} = 0.80, r_{XZ} = 0.64, r_{YZ} = 0.79$$, then square of multiple correlation coefficient $$R^{2}_{X.YZ}$$ is:
In a 3 races, 2 genders and 5 in each treatments group for two -way ANOVA, the degree of freedom for source of variation due to interaction, error and total respectively are
A random sample of size 225 is drawn from the population of mean $$\mu$$ and standard deviation $$\sigma$$. The sample mean follows the distribution with mean 100 and standard distribution 4/3. The value of $$\mu$$ and $$\sigma$$ are:
The probability of getting a total of 7 on two dice thrown together is:
Identify, from the following, the moment used as a measure of skewness?
The six decile ($$\bf{D_{6}}$$) of 5, 3, 2, 6, 8, 4 is:
The mode of the given data set is 12. The sum of the frequency on both sides of mode are 16. The skewness:
If $$X$$ and $$Y$$ represent waiting time and service time of customers in shopping mall, have joint destiny $$f(x, y) = kx ; 0 \leq y \leq x \leq 1$$, then the value of $$k$$ is
Which is not relative measures of skewness?
For two items, tea (1 kg) and sugar (1 kg), the prices in the year 2019 were ₹100 and ₹50, respectively, whereas the prices in the year 2020 were ₹125 and ₹60, respectively. The value of Laspeyres price index is:
Which of the following statements is INCORRECT?
The deseasonalised time - series data will have only trend (T), cyclical (C) and irregular (I) components and is expressed as:
For the ANOVA table
the F - statistics is
The mean deviation and coefficient of mean deviation of 5 observation are 1.2 and 0.4. If the sum of the first four terms is 10, then the fifth term is equal to:
The standard error of the given data $$15, 5, 12, 10, 20, 4$$ is
If the sum of lower and upper qualities is 6 and quartile deviation is 1.5, then the value of coefficient of quartile deviation is
The 95% confidence interval of average age of accidents in any city during last year for a sample of size 100 with mean age 34.25 from population of standard deviation 10 is
If $$r_{p}$$ be partial correlation compound on sample $$r_{AB.c}$$ compound from sample of size n, the test statistic for significance testing is
For the following frequency distribution
the value of mode is:
If the mean and variance of a binomial distribution are 5 and 4, respectively, then the value of n is:
For an experiment we have the following data set: n = 4, $$\sum_{}^{}X = a, \sum_{}^{}Y = 10, \sum_{}^{}XY = 21,\sum_{}^{}X^{2} = 30, \sum_{}^{}Y^{2} = 30$$ the correlation coefficient is -0.8 then the value of a is:
The grouped data for the observation are as follows.
The population skewness:
If each observation in a data set for number of employees in different divisions is doubled then the coefficient of quartile deviation:
If the first, second, and third moment about the origin are 2, 8, and 18 respectively, then third moment about mean is
For the variables X and Y, we collect 4 observations with $$\sum_{}^{}X = 10, \sum_{}^{}Y = 14, \sum_{}^{}X^{2} = 30, \sum_{}^{}Y^{2} = 54, \sum_{}^{}XY = 31$$ The regression line y on x is
The median of the following observations 10, 11, 9, 12, 10,10, 12, 10, 9,11 is:
For the two variables X and Y, the following observations are tabulated.
The spearman's correlation coefficient is:
If first, second, and third moment about origin are 1, 6, and 15 respectively, then Karl Pearson beta coefficient of skewness $$\beta_{1}$$ is
If mean and median of the distribution are 12 and 21, then the distribution
In a two-way ANOVA table
the value of $$x, F_{A}, F_{B}$$ are:
The median of following observations 8, 9, 10, 8, 8, 10, 8, 9 is
For the ANOVA which of the following options is INCORRECT.
The Pearson's correlation coefficient between following observation
is - 0.8. If each observation of X is halved and of Y is doubled, then Pearson's correlation coefficient equals to
For the ANOVA which option is wro1ng?
From standard pack of 52 cards, 3 cards are drawn at random without replacement. The probability of drawing a king, a queen and a jack in order is
If the second and third moment about the origin are 8 and 18 and the third moment about mean is -14 , then the first moment about the origin is:
For the random variable X with probability density function $$f(x) = \frac{(x - 3)^{2}}{5}$$; x = 3, 4, 5, the variance of X is:
If A and B are mutually exclusive, the general addition rule is:
Two random variables X and Y are said to be independent if:
The value of k so that following is probability mass function
is
If moment generating function of discrete random variable X is $$(q + pe^{t})^{n}$$, then $$E(X^{2})$$ equals to
The standard deviation of Y is double of standard deviation of X. The correlation coefficient between X and Y is 0.5. The acme angle between lines of regression is
If mean and mode of the distribution is 32 and 21, then the distribution:
To estimate the average work experience of MBA students at a management institute, five students are selected at random from each type of background, say commerce, science and engineering. This type of sampling is called:
Which of the following options is correct when data is classified on the basis of attributes?
If the third quartile of the following data set 7,10,7,8,9 is 9.5, then the value of quartile deviation is:
The arithmetic mean of the following frequency distribution of number of members in family in the society
is
The prices (in Rs.) for the commodity ABC,XYZ, MNO, and IJK in base year (2020) are 20, 18, 12, 24 and in current year (2022) are 25, 22, 15, 28 respectively. The value of price index by simple aggregative method is
The mean and median of the distribution is 12 and 15. Then the mode equals to:
The fair dice is rolled 15 times and face value are noted
The empirical probability of getting a number greater than 4 when a dice is rolled, is
If the population kurtosis of the observations 16,12,6,2,4,10 is 1.7414, then population kurtosis of the 8,6,3,1,2,5 is
Recession in industry is associated with the:
Which of the following correctly completes the given statement?
Index number helps in:
(I) determining the cost of living
(II) fixing the dearness allowances
(III) reflecting the real income
Which of the following options is INCORRECT?
Which option is incorrect?
If random variable X follows binomial distribution with parameter n and p with mean 15 and variance 10, then the value of mode is
If the first, second and third moment about origin are 2, 8 and 14. respectively, then Karl Pearson gamma coefficient of skewness $$\gamma_{1}$$ is:
If Z follows standard normal distribution with mean 0 and variance 1, then $$Z^{2}$$ follows:
Two data sets of sizes 6 and 9 have standard deviation 3 and 4, respectively, and arithmetic means 4 and 4, respectively. The standard deviation of combined data set of size 15 is:
A physical instructor claims that the mean weight of students in school is greater than 82 kg with standard deviation 20. If a sample of size 81 students is selected with mean weight of 90. The test statistic equals to
If moment generating function of continuous random variable X is $$\frac{\lambda}{\lambda - t} ; t< \lambda$$, then E($$X^{3}$$) equals to:
For frequency distribution presentation , which option is wrong.
The arithmetic mean of the following frequency distribution of number of accidents X on week working days is:
Which option is WRONG?
If $$P(A) = 0.4; P(B \mid A) = 0.05; P(C \mid A) = 0.04; P(B \mid A \cap C) = 0.09; P(C \mid A \cap B) = 0.07$$, then the probability of occurrence of all events equals to: :
If the population skewness of the observations 8,6,3, 1,2,5 is 0.233, then the population skewness of 16,12,6,2,4,10 is:
If the first, fifth and ninth decile of frequency distribution $$x_{i} \mid f_{i}$$ are 3,10,16, respectively, then Kelly's coefficient of skewness is:
For the frequency distribution of income (in lakh) of the employees in factory
the value of mode is
These seventh decile ($$D_{7}$$) of data set 4, 3, 10, 9, 1 is
For the distribution
the third factorial moment is
If the difference between the rank of the 4 observations are 2.5, 0.5, -1.5, -1.5, then Spearman's rank correlation coefficient equals to:
$$X_{1}$$ and $$X_{2}$$ represent number of occurrences of event A and 8 that follow Poisson distribution with mean rate $$\lambda_{1}$$ and $$\lambda_{2}$$, If $$Y_{1}$$ and $$Y_{2}$$ are inter-occurrence times of event A and B, then min($$Y_{1},Y_{2}$$) follows
For the distribution with unknow $$\theta$$
$$f(x, \theta) = \begin{cases}\frac{1}{\theta}; & 0 \leq x \leq \theta\\0, & elsewhere\end{cases}$$
We set the testing of hypothesis $$H_{0} : \theta = 1 \ vs \ H_{1} : \theta = 2$$. When the critical region $$X \geq 0.4$$, the value of probability of type-II error is:
For the production data
the third 3-year simple moving average is:
The grouped data for the observations are
The population skewness
For the data set
the regression coefficient $$b_{xy}$$ (y on $$x$$) equals to:
The value of a and b so that the following is probability mass function
with mean 1.1, is:
If $$A, B$$ and $$C$$ are arbitrary events, then $$P(A \cap B \cap C)$$ equals to:
If the odds in favour of any random event A are 5 : 6, then the odds against the event are:
Which of the following is the most relevant for deriving a point estimate?
For the cumulative distribution function
$$F(x) = \begin{cases}0; & x < -1\\\frac{1}{2}(x + 1)^2; & -1 \leq x \leq 0 \\1-\frac{(1-x)^2}{2}; & 0 \leq x \leq 1\\1; & 1 < x < \infty \end{cases}$$
the upper quartile point is
For ANOVA table
the F - statistics is:
If each observation is halved then the coefficient of quartile deviation
If the first quartile of data set 8,10,8,7,9 is 7.5, then the value of quartile deviation is
The interquartile range excludes ___ of the values.
For the frequency distribution of X number of grammatical mistakes per line is as follows.
The third factorial moment of X is:
If price-quantity are related for base year (0) and current year (1) are
$$\sum_{}:p_{0}q_{0} = 260,\sum_{}:p_{1} q_{0} = 395, \sum_{}:p_{0}q_{1} = 264, \sum_{}:p_{1}q_{1} = 422$$, then Marshall Edgeworth price index equals to
Which one is not non-probability sample method
If A and B are manually exclusive events such that P(A)P(B) > 0 , then which option is correct?
Which of the following is an example of using a sample to make inference about a population?
If r and R denote correlation and multiple correlation coefficient for the data set for $$X_{1},X_{2}$$ and $$X{3}$$. Which option is correct?
Which option is incorrect for the component of ti.me series.
Which one is not basis of classification of data.
The purchasing power of money is equal to:
Using the method of semi-averages, secular trend is measured when:
The mean and median of the distribution are 10 and 11 respectively, then the mode equals to
Fundamental principles of design of experiment are
(I) Randomization
(II) Replication
(III) Local control
Which option is correct?
