The prices (in ₹) of different yarns (per kg) in two consecutive years are as follows.
By simple aggregative method, the net price changes in % is:
SSC CGL Tier-2 14th September 2018 Statistics
For the following questions answer them individually
The average working hours per month of the staff aged over 50 yearsin a factory were 160 and that of the staff aged under 50 years were 210. The mean working hour per month of all the staff was 200. The ratio of the numberofthe staff aged over50 to thatof the staff aged under 50 is:
The $$4^{th}$$ decile for the given data is:
The Mean deviation about Median forthe given data.
52, 56, 66, 70, 75, 80, 82 is:
For a random variable x , the central moments $$(\mu_i)$$ of all order exist. The square of $$(2j + 1)^{th}$$ moment $$(\mu^2_{2j+1})$$ is always:
The memory-less property is followed by which of the following continuous distribution:
If the random sample of size n is drawn without replacement from finite population of size N , the correction factor for standard error of sample mean will be:
The Excess Kurtosis of the Geometric distribution with parameter p is:
Let $$\left\{X_i, i \geq 1\right\}$$ be independent and identically distributed random variables with $$P(X_i = 1) = p = 1 - P(X_i = 0), S_n = \sum_{i=1}^n X_i$$. The distribution of $$S_n$$ is:
Which one is parameter from population?
For the given figures of production of a sugar factory, the estimate of the production for 1976 using straight line trend with origin at the year 1972 by the least squares method $$\left(\sum x = 0, \sum x^2 = 28, \sum xy = 56\right)$$ is:
Which of the following methods is NOT used in computation of a seasonalindexfor time series?
The second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson’s coefficient of skewness $$\beta_2$$
For the study purpose, the mean ofthe observations is 148 gm andstandard deviation is 17.4 gm. Approximately, the coefficient of variation equals to:
The variance of degenerate random variable is:
Statistics is not applicable to ........... observation.
The mode (correct to two decimal places) for the given data is:
Which of the following is NOT a wayof the sampling?
Five persons A, B, C, D and E occupy seats in a row at random. The probability that A and B sit next to each other is:
A Poisson distribution has a double mode at x = 1 and x = 2. The probability for x = 1 or for x = 2 of these two values is:
With reference to index numbers, which of the following statements is true?
If a discrete random variable X follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20, the value of $$P(\mid X - 14 \mid < 5)$$ will be:
Marshall-Edgeworth Index number:
The curve obtained by joining the points, whose x-coordinates are the upper limits of the class interval and y-coordinates are corresponding cumulativefrequencies is called:
The probability density function of a random variable X is $$f(x) = \frac{\pi}{10} \sin \frac{\pi x}{5}; 0 \leq x \leq 5$$. The first quartile of X is:
60% of the employees of a companyare college graduates. Of these, 10% are in sales. Of the employees who did not graduate from college, 80% are in sales. The probability that an employee selected at randomisin sales, is:
By the method of moving averages, the seasonal index for four quarters equals to:
If $$r_{12} = +0.80, r_{13} = -0.40$$ and $$r_{23} = -0.56$$, then the square of multiple correlation coefficient (correct to four decimal places) $$R^2_{1.23}$$ is equal to:
If the multiple correlation coefficient of $$X_1$$, on $$X_2$$, and $$X_3$$ is zero, then:
The null hypothesis in ANOVA one-way classification, the study of the variances due to k different sources, is:
The limits of multiple correlation coefficient $$R_{1.23}$$ are:
Second differencing in time series can help to eliminate which trend?
(I) Quadratic trend
(II) Linear trend
The probability of getting 9 cards of the samesuit in one hand at a game of bridge is:
Which of the following is NOT an approach for assigning the probability of the event?
A, B, and C are three mutually exclusive and exhaustive events associated with a random experiment. If $$P(B) = \frac{3}{2}P(A)$$ and $$P(C) = \frac{1}{2}P(B)$$ then value of $$P(A)$$ is:
If Laspeyres price index of a commodity is 208 and Passche’s price index of the same commodity is 52, the value of Fisher index number will be:
Following two statements are related to regression coefficient
(1) Independentof the changeoforigin
(II) Independentof the changeofscale
For the recorded observation, the coefficient of variation is 0.2 and the variance is 16. The arithmetic mean is:
If X has Binomial distribution with parameters $$n$$ and $$p$$ such that $$np = \lambda$$ then $$\lim_{n \rightarrow \propto}b(x, n, p);x = 0, 1, 2, ....$$ is equal to:
The given table shows ANOVA two-way classification to test two types of cloths in fashion trends.
The respective values (correct to two decimal places) of $$(\alpha, \beta, \gamma)$$ are:
The arithmetic mean of marks of the students for the given data is:
The approximate median of the Poissondistribution with parameter $$\lambda$$ is:
If $$X_1, X_2, ...... X_n$$ is a simple random sample without replacement of size n from a finite population of N units with mean $$\mu$$ and $$\sigma^2$$, the covariance of $$(X_i, X_j)$$ will be:
Which of the following approaches does multiplicative model have for the component of Time series Secular trend (T) , Seasonal variation (S) , Cyclical fluctuation (C) and Irregular movement(I) ?
Let x and y be two variables with variance as 1990 and 796 with 11 and 9 number of observations respectively. The value of F(10, 8) at 5% level of significance is:
If Arithmetic mean and coefficient of variation of x are 10 and 40 respectively, then the variance of y = 10 - 2x is:
Let MSA defines mean sum of squares due to factor A and MSE defines mean sum of squares dueto error. If the null hypothesis of ANOVA for one way classification is not true, then $$\frac{E(MSA)}{E(MSE)}$$ is:
As per the given data, Laspeyres price index for the year 2006 is:
If $$Z_1, Z_2, ..., Z_n$$ are $$n$$ independent standard normal variates, then $$\sum_{i=1}^n Z^2_i$$ will follow:
The coefficient of correlation is r between X and Y having standard deviation $$\sigma_x$$ and $$\sigma_y$$ . The tangent of the angle
between two lines of regression is:
The incomes of the employees in a state is assumed to be normally distributed with mean ₹15,000 and variance ₹900. The median of the distribution of the income is:
For a normal distribution, which of the following is true?
The mode of a geometric distribution with parameter p is:
Let $$M, M_d, M_o$$ denote mean, median and mode and $$Q_1, Q_2$$ and $$Q_3$$ quartile points. Which of the following is an absolute measure of skewness?
The second quartile for the following data 38, 39, 40, 52, 59, 67, 73, 77, 149, 248 is:
With reference to analysis of variance, which of the following statements is/are correct?
(I) Change of origin will affect the value of F .
(II) Change of scale will affect the value of F .
Which of the following is a sources of primary data?
For a distribution with mean, median, mode and standard deviation 25, 24, 26 and5 respectively, Karl Pearson’s coefficient of skewness equals to:
The product of partial regression coefficient $$b_{12.3} b_{23.1} b_{31.2}$$ equals to:
If $$x_i \mid f_i, i = 1, 2, ..... n$$ is a frequency distribution with standard deviation 15 and mean 30,the coefficient of variation will be equal to:
At a reservation counter, passengers are arriving for booking the tickets in a Poisson fashion with mean rate 60 per hour. The kurtosis of the inter-arrival times of the passengers is:
Completely randomised design is based on the principles of .......... and randomisation only.
If $$\sum p_oq_o = 160, \sum p_oq_1 = 250, \sum p_1q_o = 200$$, and $$\sum p_1q_1 = 288$$ then Fisher ideal index number is equal to:
Completely Randomised Design provides maximum numberof degree of freedom for the:
At a round table, n persons are seated on n chairs. The probability that two friends from same college are sitting next to each other, is:
If $$p(x) = \begin{cases}{\frac{x}{15};} & x = {1, 2, 3, 4, 5}\\0;& elsewhere\end{cases}$$, the probability $$P\left\{\frac{1}{2} < X < \frac{5}{2}\right\}$$ is equal to:
The first four moments of a distribution about the origin are -1.5, 17, -30 and 108. The third moment about the mean is:
Let $$M, M_d, M_o, Q_1, Q_2, Q_3$$ be the mean, median, mode and quartile points for different data points. Skewness is negative if:
A dice was thrown 400 times and ‘six’ resulted 80 times. The data is used to justify the hypothesis of an unbiased dice at 95% confidence. With reference to the given case, which of the following statements is correct?
The sample sizes for two cases were 15 each with means as 104 and 114 respectively and variances as 290 and 510 respectively. Let the null hypothesis is that the two population means are equal, then the value of t-statistic is:
The variation among the observations of each specific class is known as:
If $$n_1 = 10$$ and $$n_2 = 5$$, are the sizes, $$\overline{x}_1, = 7$$ and $$\overline{x}_2, = 4$$ are the means and $$\sigma_1 = 1$$ and $$\sigma_2 = 1$$ are the standard deviations of two series of data. If combined mean $$\overline{x}_2, = 6$$, then the variance of the combined series with size $$n_1 + n_2$$ is equal to:
The empirical relation between mean $$(M)$$ , median $$(M_d)$$ , and mode $$(M_o)$$ is:
X and Y are independent normal variables with mean 50 and 80 respectively and standard deviation as 4 and 3 respectively. What is the distribution of X + Y ?
The coefficient of correlation is the .......... of coefficients of regression.
Which of the following satisfies the time and factor reversal test?
For a distribution, mean is 40, median is 40.5 and modeis 41. The distribution is:
The following observations 14, 19, 17, 20, 25 constitute a random sample from an unknown population with mean $$\mu$$ and standard deviation $$\sigma$$. The point estimation of population mean is:
The mean deviation from an average A will be minimum, if A represents:
A man pedals cycle from his house to his office at a speed of 10 km/h and back from the office to his house at a speed of 15 km/h. H is average speed (in km/h) is:
For a distribution, the mean is 10, variance is 16, $$\gamma_1$$ is +1 and $$\beta_2$$ is 4. The distribution is:
The problem of statistics is given in two sections of same standard. The odds against for section X to solve the problem are 4 : 3 and odds in favour to section Y for solving the same problem are 7 : 8. The probability that neither section solves the problem of statistics. if both sections try independent of each other, is:
If the marks obtained by 500 candidates in statistics paper is given below, then the lower quartile mark is:
$$\mu'_{(r)}$$ and $$\mu'_r$$ represent the factorial moment of order r about the origin and $$r^{th}$$ moment about the origin of the distribution $$x_i \mid f_i,i = 1,2,...n$$. The value of $$\mu'_2$$ equals to:
For making frequency distribution, the number of classes used depends upon:
If the independent random variables X,Y are Binomially distributed with $$n = 3, p = \frac{1}{3}$$ and $$n = 5, p = \frac{1}{3}$$ respectively, then the probability of $$(X + Y \geq 1)$$ is:
With which characteristic movement of a time series would you associate increasing demand of smaller automobiles ?
For the discrete distribution, the Pearson’s coefficient of skewness $$\beta_2$$ is always:
The square of normal variate with mean 0 and variance 1 follows:
Approximately, the coefficient of variation for the given data where Pearson’s second measure of skewness = 0.42, arithmetic mean = 86 and median = 80, is:
In one way ANOVA, $$\sigma^2$$ is estimated by:
If ten coins are tossed simultaneously, then the probability of getting at most 1 head is:
Which of the following is NOT a type of data classification?
If the occurrence of events follows Poisson Process with mean rate $$\lambda$$ , then inter-occurrence time of events will follow:
A random sample of 100 ball bearings selected from a shipment of 2000 ball bearing has an average diameter of 0.354 inches with standard deviation 0.048 inches. The 95% confidence interval for the average diameter of these 2000 ball bearings is:
The median for the given frequency distribution is:
In Spearman rank correlation coefficient $$r_s = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}$$, the maximum value of $$\sum d^2$$ in case of untied ranks is:
If $$x = X - \overline{X}$$ and $$y = Y - \overline{Y}$$ and the number of pairs $$(X,Y)$$ is n, then the Karl Pearson’s coefficient of correlation is:
For a group of 100 students, the mean andstandard deviation of scores were found to be 30 and 5 respectively. Later on it was discovered that the scores 34 and 53 were misread as 43 and 35 respectively. The corrected mean equals to:
The given table shows the ranking of ten students in two subjects mathematics and statistics.
The coefficient of rank correlation is:
