Statistics · JEE Main previous year questions

Let $x_1,x_2,\dots ,x_n$ be $n$ observations such that $$\sum x_i^2=400\text{ and }\sum x_i=80.$$ Then a possible value of $n$ among the following is

1. A.$18$
2. B.$15$
3. C.$12$
4. D.$9$

Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of change of origin and scale. Which of these is/are correct?

1. A.only (a)
2. B.only (b)
3. C.only (a) and (b)
4. D.(a), (b) and (c)

In a series of 2n observations, half of them equal $a$ and remaining half equal $-a$. If the standard deviation of the observations is 2, then $|a|$ equals

1. A.2
2. B.$\sqrt{2}$
3. C.$\frac{1}{n}$
4. D.$\frac{\sqrt{2}}{n}$

The mean and the variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of $2$ successes is :

1. A.$\frac{28}{256}$
2. B.$\frac{219}{256}$
3. C.$\frac{128}{256}$
4. D.$\frac{37}{256}$

A dice is tossed $5$ times. Getting an odd number is considered a success. Then the variance of distribution of success is :

1. A.$8/3$
2. B.$3/8$
3. C.$4/5$
4. D.$5/4$