Sample QuestionsStatistics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The wickets taken by a bowler in a one day cricket match are $4, 5, 6, 3, 4, 0, 3, 2, 3, 5.$ The mode of the data is $...........$
Answer: A.
View full solution →The average of the first five odd prime numbers is:
Answer: B.
View full solution →Mode of the distribution is that value of the variate for which the $..........$ is $..........$
- ✓
- B
- C
frequency, arithmetic mean
- D
frequency, arithmetic mean
Answer: A.
View full solution →The average age of $6$ students is $11$ years. If two more students of age $14$ and $16$ years join, their average will become
- A
$13$ years
- ✓
$12$ years
- C
$12\dfrac{1}{2}$ years
- D
$12\dfrac{1}{2}$ years
Answer: B.
View full solution →If the mean of $x + 2, 2x+ 3, 3x + 4, 4x + 5$ is $x + 2$ then $x$ is equal to:
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ Consider the following data
| $x_i$ |
$5$ |
$10$ |
$15$ |
$20$ |
$25$ |
| $f_i$ |
$7$ |
$4$ |
$6$ |
$3$ |
$5$ |
Then, the mean deviation about the mean is $6.32.$
Reason $(R)$ Consider the following data.
| $x_i$ |
$10$ |
$30$ |
$50$ |
$70$ |
$90$ |
| $f_i$ |
$4$ |
$24$ |
$28$ |
$16$ |
$8$ |
Then, the mean deviation about the mean is $15.$ - A
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A.$
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- ✓
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ The average marks of boys in a class is $52$ and that of girls is $42.$ The average marks of boys and girls combined is $50.$ The percentage of boys in the class is $80\%.$
Reason $(R)$ Mean marks scored by the students of a class is $53.$ The mean marks of the girls is $55$ and the mean marks of the boys is $50.$ The percentage of girls in the class is $64\%.$
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A.$
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- ✓
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ Tf the mean of $n$ bservations $1^2, 2^2, 3^2, ..., n^2 $ is $\frac{46\text{x}}{11},$ then nis equal to $11.$
Reason $(R)$ For two data sets each of size $5,$ the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4,$ respectively. The variance of combined data set is $\frac{11}{2}.$
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A$.
- ✓
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ If each of the observations $x_1, x_2, ..., X_n $ is increased by a, where ais a negative or positive number, then the variance remains unchanged
Reason $(R):$ Adding or subtracting a positive or negative number to $($or from$)$ each observation of a group does not affect the variance.
- ✓
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A.$
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Consider the following data
| $x_i$ |
$60$ |
$61$ |
$62$ |
$63$ |
$64$ |
$65$ |
$66$ |
$67$ |
$68$ |
| $f_i$ |
$2$ |
$1$ |
$12$ |
$29$ |
$25$ |
$12$ |
$10$ |
$4$ |
$5$ |
Assertion $(A):$ The mean of the data using shortcut method is $32.$
Reason $(R):$ The standard deviation of the data using shortcut method is $1.69.$ - A
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- ✓
$A$ is false; $R$ is true.
Answer: D.
View full solution →The mean and standard deviation of $20$ observation are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in cases of it is replaced by $12 .$
View full solution →The mean and standard deviation of $20$ observation is found to be $10$ and $2$ respectively. On rechecking, it was found that observation $8$ was incorrect. Calculate the correct mean and standard deviation in cases of the wrong items is omitted.
View full solution →Find the mean and variance of the following data.
| $x_i$ |
$92$ |
$93$ |
$97$ |
$98$ |
$102$ |
$104$ |
$109$ |
| $f_i$ |
$3$ |
$2$ |
$3$ |
$2$ |
$6$ |
$3$ |
$3$ |
View full solution →Find the mean and variance for each of the data
| $x_i$ |
$6$ |
$10$ |
$14$ |
$18$ |
$24$ |
$28$ |
$30$ |
| $f_i$ |
$2$ |
$4$ |
$7$ |
$12$ |
$8$ |
$4$ |
$3$ |
View full solution →Find the mean and variance for: First $10$ multiples of $3$
View full solution →Find the mean and variance for each of the data First $n$ natural numbers.
View full solution →Find the mean and variance for each of the data
$6, 7, 10, 12, 13, 4, 8, 12$
View full solution →Fill in the blanks.
If the variance of a data is 121, then the standard deviation of the data is _______.
Fill in the blanks.
The sum of the squares of the deviations of the values of the variable is _______ when taken about their arithmetic mean.
Fill in the blanks.
If $\bar{\text{x}}$ is the mean of n values of x, then $\sum\limits^{\text{M}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})$ is always equal to _______. If a has any value other than $\bar{\text{x}}$ then $\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})^2$ is _______ then $\sum(\text{x}_\text{i}-\text{a})^2$
View full solution →Fill in the blanks.
The standard deviation is _________ to the mean deviation taken from the arithmetic mean.
Fill in the blanks.
$\text{Cofficient of variation}=\frac{......}{\text{Mean}}\times100$
View full solution →The mean and standard deviation of a group of $100$ observation were found to be $20$ and $3$ respectively. Later on it was found that three observations were incorrect, which were recorded as $21, 21$ and $18$. Find the mean and standard deviation if the incorrect observations are omitted.
View full solution →The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard deviation | 12 | 15 | 20 |
Which of these three subjects shows the highest variability in marks and which shows the lowest?
Given that $\bar{x}$ is the mean and $\sigma^2$ is the variance of n observations $x_1, x_2, \ldots x_n$ Prove that the mean and variance of the observation $ax _1, ax _2, \ldots . ax _{ n }$ are $a \bar{x}$ and $a ^2 \sigma^2$ respectively $(a \neq 0)$
View full solution →The mean and standard deviation of six observation are $8$ and $4$ respectively. If each observation is multiplied by $3$, find the new mean and new standard deviation of the resulting observations.
View full solution →The mean and variance of $7$ observations are $8$ and $16$ respectively. If five of the observations are $2, 4, 10, 12, 14$ find the remaining two observations.
View full solution →