If $$Q_{3} - Q_{2} > Q_{1}$$ , the value of Bowley's coefficient of skewness is:
SSC CGL Tier 2 28th January 2022 Statistics
For the following questions answer them individually
Rohit wants to check his IQ with an MCQ test. The test has five questions with one correct answer. Each question has three options. If he just randomly guesses the answer to each question, what is the probability that he will get exactly three questions correct?
For the uniformly distributed random variable X with a = 0 and b = $$\theta$$, the value of the ratio of raw moments $$\left(\frac{\mu_{3}}{\mu_{4}}\right)$$ is:
If $$n_{1} = 10,n_{2} = 5$$ are the sizes of a male and female student group with mean ages $$\overline{x_{1}} = 10, \overline{x_{2}} = 4$$, respectively, with an equal standard deviation $$\sigma_{1} = 1, = \sigma_ 2$$ the standard deviation of the combined series with size $$n_{1} + n_{2} $$, and combined mean $$\overline{x} = 8$$ is equal to:
For the given distribution of female weight in a colony, the quartiles are 60.1, 61.3, 62.6. The value of Bowley's coefficient of skewness is:
The average income of a worker for the first five days of the week is ₹25 per day. If he works for the first six days of the week, his average income per day is ₹30. His income for the sixth day is:
The regression assumption is that the deviations from the regression line (residuals) follow a:
If the two lines of regression are x + 2y- 5 = 0 and 2x + 3y - 8 = 0 . the means of X and Y are:
If the mean, median, mode and standard deviation for the distribution are 61.4, 61.25, 61.13, 1.76, respectively, Karl Pearson's first coefficient of skewness equals to:
Multiple regression equation of $$X_{1}$$ on $$X_{2}$$ and $$X_{3}$$ is $$\left(X_{1} -\overline{X}_{1}\right) = b_{12.3}\left(X_{2} -\overline{X}_{2}\right) + b_{13.2}\left(X_{3} -\overline{X}_{3}\right)$$ where $$ b_{13.2}$$ is:
The prices (in ₹) of vegetables (per 5 kg) in the years 2019 and 2020 are as follows:
2019: 60 (Potato); 70 (Onion); 40 (Tomato); 30 (Chilli)
2020: 70 (Potato); 60 (Onion); 48 (Tomato); 27 (Chilli)
By the simple aggregative method, the net price changes in percentage are:
If the first, second, and third quartiles of the distribution are 24. 42. and 72, respectively, the quartile deviation equals to:
A study based on complete enumeration is known as:
Let X be a discrete random variable with pmf $$\left(x\right) = \frac{\left(x - 3\right)^{2}}{5}$$, x = 3,4,5 . The variance of X is:
If the regression line of Y on X and that of X on Y are perpendicular to each other, then the value of correlation coefficient r(X,Y) is given by:
If, for two independent events A and B, P(A) = 0.8 and P(B) = 0.6, then the probability of their simultaneous occurrence is:
The individual probabilities of the occurrence of two events A and B are known. The probability of occurrence of both the events together will be:
The mode of a distribution is 4 and its standard deviation and coefficient of variation are given by 9 and 4.4, respectively. Find the value of Pearson's coefficient of skewness.
The coefficient of quartile deviation of the data set 3, 5 7, 8, 12, 13, 14, 18, 21, is:
Based on the given data, what is the correlation coefficient between the variables X and Y?
Which two of the following quantities are sample statistics?
'Linseed crops badly spoiled on account of rains' is an example of which option:
A sample of 30 latest, returns on UTI stock with unknown standard deviation reveals a mean return of $4. The estimated standard error of the sample means is 0.02. How much more of the sample (approximately) should be added to reduce the standard error of the sample mean to 0.01?
By the method of moving averages, the seasonal index for four quarters equals to:
The coefficient of mean deviation about median equals to:
If the Standard deviation of a data is 10 and Coefficient of Variation is 50, then the mean of the data is:
The lower quartile of $$f\left(x\right) = \frac{1}{12}\left(5-2x\right); -1 \leq x \leq 2$$ is one root of the quadratic equation:
Which variable type is required to be used more than once in factorial design?
The following measures were computed for a non-symmetrical frequency distribution: mean = 50, coefficient of variation = 35% and Karl Pearson's coefficient of skewness of first type= -0.25. The value of mode of the distribution is:
For the PDF $$f\left(x\right) = \frac{x}{4}; 1< x < 3$$, the $$50^{th}$$ percentile is:
If the exponential distribution is given as $$f\left(x\right) = x^{-x};0 \leq x \leq \infty$$, then the Pearson's constant $$\beta_{1}$$ (excess kurtosis) is:
For ANOVA two-way classification to test two types of cloth in fashion trends, we have the following table.
The value of $$\gamma$$ is:
Boy child is more probable than girl child to a couple in 2019. A random sample found 224 boys were born among 400 newborn children. For this sample evidence that the birth of boys is more common than the birth of girls in the entire couple population, the value of test statistics is:
We measure ten units from the latest production lot to measure the length of the product that gives the sample mean to be 17.55 inches, and the sample standard deviation to be 1.0 inch. The 95%, confidence interval for the population mean is:
The cost of living index numbers are used to determine actual salaries by the procedure of:
Which of the following options is NOT an example of absolute measures of dispersions?
In averaging the price relatives, which of the following options is the most appropriate average?
If each group comprises of one observation only, the value of the correlation ratio is:
For a randomised block design ANOVA test with 5 treatments group and 6 blocks, the error degrees of freedom are:
The median of a Weibull distribution with shape parameter k and scale parameter $$\lambda$$ is:
The moving averages for the trend of exponential type are to be computed by using:
The mean deviation about mean of the data 3, 6, 6, 7, 8, 11 , 15, 16, is:
If X follows the normal distribution with mean $$\mu$$ and variance $$\sigma^{2}$$, the fourth moment about origin is:
The television habits of 30 children were observed. The sample mean was found to be 8.2 hours per day, with a standard deviation of 2.4 hours per day. You tested the claim that the standard deviation was at least 6 hours per day. The value of the test statistics is:
The median of the series 2, 17, 6, 19, 10, 11, 8, 16, 21, is:
The mode of dataset 5-10, 10-15, 15-25, 25-35, 35-50, 50-60 with frequency of each class 2, 6, 10, 22, 27, 11, respectively, is:
The ANOVA was used to test the results of three drug treatments. Each drug was applied to 20 patients. The MSE for this study was 16. What is the estimate of the population standard deviation for all 60 patients sampled for this study?
A random variable X possesses the following function.
The value of E(X) is:
Analysis of variance is a statistical process of comparing the of yield under several treatments.
In a tri-variate population $$\gamma_{12} = 0.7, \gamma_{13} = 0.6$$ and $$ \gamma_{23} = 0.5$$, then the value of $$R^{2}_{1,23}$$ is:
A number is selected randomly from each of the given two sets.
Set 1: 1 , 2, 3, 4, 5, 7, 8
Set 2: 2, 3, 4, 5, 6, 7, 8, 9
The probability that the sum of the numbers is equal to 9 is:
Let there be no overlap between the box and whisker plots for three drug treatments where each drug was administered to 35 individuals. The box plots for this data:
The secular trend is depicted by the method of semi-averages when:
The mean absolute deviation for 11, 16, 16, 18, 19, 22, is:
Which distribution has the same mean, median and mode?
In a library, there are 40% mathematics books and the remaining 60% are science books. It is known that 2% of the mathematics books are in Hindi, and 1% of the science books are in Hindi. If one book is taken out at random and is found to be in Hindi, the probability that it is a science book is:
If $$A_{1}, A_{2}, A_{3}$$ are three mutually exclusive events, the probability of their union is equal to:
Which of the following options is correct?
Suppose that the CDF of X is given by $$f\left(x\right) = \begin{cases}0;x < 0 &\\\frac{1}{5};0\leq x <2 & \\\frac{2}{5};2\leq x <4 \\ 1; x \geq4 \end{cases}$$
The value of P(X = 4) is:
If Laspeyre's index is 128 and Paasche's index is 32, then Fisher's ideal index is approximately equal to
The regression coefficient is independent of:
(I) Origin
(II) Scale
For the data on early earning of employees in a company, the raw moments about some arbitrary poim A = 12 is given by $$\mu_{1} = -3, \mu_{1} =94, \mu_{3} = 546, \mu_{3} = 2200$$. The moment $$\mu_{3}$$ about actual mean 94 is:
The difference between kurtosis and excess kurtosis is:
Let X and Y be two jointly continuous random variables with joint pdf $$f_{xy}\left(x,y\right) = Cx^{2}y;0 \leq y \leq x \leq 1$$. The value of constant C is:
Let X and Y be independent random variables that denote the number of virus 1 and virus 2, respectively, in one room, follow Poisson distribution with parameter $$\lambda_{1} = 1 $$ and $$\lambda_{2} = 2 $$ respectively. The expected number of viruses in the room is:
Which of the following is NOT a nominal data?
The skewness of geometric variates with $$\rho = 0.75$$ is:
For qualitative sampling, which method among the following is generally used?
In ANOVA, the value of statistic F lies in the range:
The power of a test can be improved by:
In Spearman rank correlation coefficient $$ r_{s} = 1-\frac{6\sum d^{2}}{n\left(n^{2}-1\right)}$$, the maximum value of $$\sum d^{2}$$ in case of untied ranks is:
If X is a random variable with PDF $$f\left(x\right) = \frac{x^{2}}{9}; 0 < x < 3$$ the cumulative contribution function of $$Y = X^{5}$$
Calculate the seventh decile of the following data set.
23, 31, 26, 31 , 22, 63, 44, 78, 61 , 64, 35, 54, 57, 35, 73, 55, 50, 31 , 56, 32, 41 , 55, 29
The change in the prices and quantities of each individual commodity are summarised as follows:
The Laspeyres Price Index for the year 2017. using the year 2016 as the base year, is:
The error deviations within the sum of square for error statistic measure variations is:
In the absence of skewness, the coefficient of skewness by Karl Pearson $$\left(S_{k}\right)$$, Bowley's $$\left(S_{q}\right)$$ and by Kelly's $$\left(S_{p}\right)$$ are:
If X and Y are two random variables such that their expectations exist and $$P(X \leq Y) = 1$$, then which of the following opctons is true?
If X is negative binomially distributed with r =10 and p = 0.4, the skewness of X is:
For the given distribution, what is the value of the fourth moment?
If $$x_{i}\mid f_{i}$$, i = 1,2, ... n is frequency distribution with variance 4, mode 4, and arithmetic mean 2.5, then the mean square deviation from the mode is:
If X follows a Poisson distribution with parameter $$\lambda = 0.2$$, the fourth factorial moment of X is:
For the joint density $$f_{xy}\left(xy\right) = x + \frac{3}{2}y^{2};0\leq x \leq 1,0 \leq y \leq 1$$, the value of $$P\left(0 \leq Y \leq \frac{1}{2}\mid 0 \leq X \leq \frac{1}{2}\right)$$ is:
In the completely randomised design, the variance between columns depicts the difference between the ___ of each group and the ___
For positive data series, the relative position of arithmetic, geometric and harmonic mean is:
In a class of 50 students, 10 have failed and their average of marks is 2.5. The total of marks secured by the entire class is 285. find the average marks of those who have passed.
Given that $$P\left(A\right) = 1/3, P\left(B\right) = 1/4, P\left(A\mid B\right) = 1/6$$, the probability $$ P\left(B\mid A\right)$$ is equal to:
The number of class intervals in a frequency table does NOT depend on:
If the Bowley's coefficient of skewness $$S_{q}$$ is positive, which of the following options is correct?
The first four raw moments of distribution are 2, 136, 320 and 40.000. The coefficient of kurtosis is:
Which of the following is NOT an advantage of tabulation?
If a random sample of size n is drawn without replacement from a finite population of size N ,the correction factor for standard error of sample mean is:
The observed value $$x$$ = 13.7 belongs to which quartile if continuous random variable X follows a uniform distribution with a = 5 and b = 22?
The workers at a large manufacturing company can earn monthly bonuses. The distribution of monthly bonuses earned by all workers last year has a mean of 2.3 and a standard deviation 1.3. Let Z represent the standard normal distribution. If X represents the mean of monthly bonuses earned last year for a random sample of 40 workers. which of the following gives the approximate probability that X is less than 2?
The multiplicative model of the time series is:
The geometric mean for the data set having negative observations:
For ten students, the Spearman's rank correlation coefficient between scores in two different subjects is - 0.3. The value of the sum of the square of the difference of ranks is:
What two pieces of information are needed at given level of significance for the determination of the critical value for testing whether the test statistic of ANOVA is statistically significant?
Which distribution has the same mean and variance?
The profit of a company during the first five months of a year is ₹Ninety-six lakhs per month and during the last seven months is ₹120 lakhs per month. The average profit per month during the whole year is:
_________ is a plot of a sequence of observations made over time.
