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Which two of the following statements are true?  a) The sum of the deviations from mean (ignoring algebraic signs) is greater than the sum of the deviations from median (ignoring algebraic signs)  b) Standard deviation is independent of change of origin and change of scale  c) In a symmetrical distribution, mean deviation equals 4/5 of standard deviation  d) In a symmetrical and bell shaped distribution quartile deviation is 1/3 of standard deviation  Choose the correct answer from the options given below
Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.
Consider the following statements regarding inspection and quality control: 1. Coefficient of variation is a relative measure of dispersion. 2. Standard deviation is the root mean square of the deviation of all the results. 3. Standard deviation is relative measure of dispersion. 4. Lower value of standard deviation indicates low degree of uniformity of observations. Which of the above statements are correct?
A class of first year B. Tech. students is composed of four batches A, B, C and D, each consisting of 30 students. It is found that the sessional marks of students in Engineering Drawing in batch Chave a mean of 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are 5.5 and 4.2, respectively. It isdecided by the course instructor to normalize the marks of the students of all batches to have the same mean and standard deviation as that of the entire class. Due to this, the marks of a student in batch C are changed from 8.5 to
Which two of the following statements are true?  a) Skewness studies the flatness or peakedness of the distribution  b) A positively skewed distribution curve is stretched more to the right than to the left  c) On the basis of empirical relationship between mean, mode and median for moderately asymmetrical distribution, Karl Pearson's coefficient of skewness can be measured by 3 (Mean -Median) divided by Standard Deviation  d) If mean < mode, the distribution is positively skewed  Choose the correct option from those below: 
A company recruits candidates satisfying the following criteria -  1. Candidates who secured at least 85% in standard 10th or equivalent. 2. Candidates who secured at least 65% in standard 12th or equivalent. 3. Candidates who are not from commerce background. Who among the following candidates will the company definitely select? A. Jitesh is a science student having scored 70% in standard 12th and 80% in 10th with an excellent sports background. B. Jignesh scored 80% in standard 12th, 90% in standard 10th and secured 2nd place in his college among all commerce students. C. Jayesh scored 75% in standard 10th, 75% in standard 12th and is an arts student. D. Jinesh secured 80% in standard 12th, 88% in standard 10th and is a science student with great acting skills
Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2) the standard deviation of Y is
Consider the continuous random variable with probability density function
f(t) = 1 + t for -1 ≤ t ≤ 0
      = 1 - t for 0 ≤ t ≤ 1
The standard deviation of the random variable is
The standard normal cumulative probability function (probability from $$ - \infty $$  to xn) can be approximated as $${\text{F}}\left( {{{\text{x}}_{\text{n}}}} \right) = \frac{1}{{1 + {\text{exp}}\left( { - 1.7255{{\text{x}}_{\text{n}}}{{\left| {{{\text{x}}_{\text{n}}}} \right|}^{0.12}}} \right)}}$$       where xn = standard normal deviate. If mean and standard deviation of annual precipitation are 102 cm and 27 cm respectively, the probability that the annual precipitation will be between 90 cm and 102cm is
Random variable X is normally distributed, with a mean of 25 and a standard deviation of 4. Which of the following is the approximate interquartile range for this distribution?