Statistics - Maharashtra Board STD 11 Maths Questions

Q 1MCQ1 Mark

The standard deviation of first $10$ natural numbers is :

A
$5.5$
B
$3.87$
C
$2.97$
✓
$2.87$

Answer: D.

Q 2MCQ1 Mark

Let $a, b, c, d, e$ be the observations with mean m and standard deviation $s$. The standard deviation of the observations $a + k, b + k, c + k, d + k, e + k$ is:

✓
$s$
B
$ks$
C
$s + k$
D
$\frac{\text{s}}{\text{k}}$

Answer: A.

View full solution →

Q 3MCQ1 Mark

If $n = 10, \overline{\text{X}}=12$ and $\sum\text{x}_\text{i}^2=1530,$ then the coefficient of variation is :

A
$36\%$
B
$41\%$
✓
$25\%$
D
None of these

Answer: C.

View full solution →

Q 4MCQ1 Mark

Let $x_1, x_2, ..., x_n$ be n observations. Let $y_i = ax_i + by_i$ + b for $i = 1, 2, 3, ..., n$, where a and b are constants. If the mean of $x_i's$ is $48$ and their standard deviation is $12$, the mean of $y_i's$ $55$ and standard deviation of $y_i's$ is $15$, the values of a and b are:

✓
$a = 1.25, b = -5$
B
$a = -1.25, b = 5$
C
$a = 2.5, b = -5$
D
$a = 2.5, b = 5$

Answer: A.

View full solution →

Q 5MCQ1 Mark

If the standard deviation of a variable $X$ is $\sigma,$ then the standard deviation of variable $\frac{\text{aX+b}}{\text{c}}$ is :

A
$\text{a}\ \sigma$
B
$\frac{\text{a}}{\text{c}}\sigma$
✓
$\Big|\frac{\text{a}}{\text{c}}\Big|\sigma$
D
$\frac{\text{a}\sigma+\text{b}}{\text{c}}$

Answer: C.

View full solution →

Q 6Solve the following Question.(1 Marks)1 Mark

If $x_1, x_2, ..., x_n$ are n values of a variable $X$ and $y_1, y_2, ..., y_n$ are $n$ values of variable $Y$ such that $y_i = ax_i + b, i = 1, 2, ..., n,$ then write Var$(Y)$ in terms of Var$(X)$.

View full solution →

Q 7Solve the following Question.(1 Marks)1 Mark

If the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write the value of standard deviation.

View full solution →

Q 8Solve the following Question.(1 Marks)1 Mark

If $X$ and $Y$ are two variates connected by the relation $\text{Y}=\frac{\text{aX+b}}{\text{c}}$ and $\text{Var}(\text{X})=\sigma^2,$ then write the expression for the standard deviation of $Y$.

View full solution →

Q 9Solve the following Question.(1 Marks)1 Mark

If a variable $X$ takes values $0, 1, 2,..., n$ with frequencies $^nC_0, ^nC_1, ^nC_2 , ... , ^nC_n$, then write variance $X$.

View full solution →

Q 10Solve the following Question.(1 Marks)1 Mark

If each observation of a raw data whose standard deviation is $\sigma $ is multiplied by a, then write the S.D. of the new set of observations.

View full solution →

Q 11Solve the Following Question.(3 Marks)3 Marks

Two plants A and B of a factory show following results about the number of workers and the wages paid to them:

	Plant A	Plant B
No. of workers	5000	6000
Average monthly wages	₹ 2500	₹ 2500
Variance of distribution of wages	81	100

In which plant A or B is there greater variability in individual wages?

View full solution →

Q 12Solve the Following Question.(3 Marks)3 Marks

The means and standard deviations of heights ans weights of 50 students of a class are as follows:

	Weights	Heights
Mean	63.2kg	63.2 inch
Standard deviation	5.6kg	11.5 inch

Which shows more variability, heights or weights?

View full solution →

Q 13Solve the Following Question.(3 Marks)3 Marks

Find the mean variance and standard deviation for the following data:
$2, 4, 5, 6, 8, 17.$

View full solution →

Q 14Solve the Following Question.(3 Marks)3 Marks

Find the mean variance and standard deviation for the following data:
$15, 22, 27, 11, 9, 21, 14, 9.$

View full solution →

Q 15Solve the Following Question.(3 Marks)3 Marks

Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

View full solution →

Q 16Solve the Following Question.(4 Marks)4 Marks

Calculate mean deviation about median age distribution of $100$ persons given below:

Age	$16-20$	$21-25$	$26-30$	$31-35$	$36-40$	$41-45$	$46-50$	$51-55$
No. of persons	$5$	$6$	$12$	$14$	$26$	$12$	$16$	$9$

View full solution →

Q 17Solve the Following Question.(4 Marks)4 Marks

Find the mean deviation from the median for the following data:

$x_i$	$15$	$21$	$27$	$30$
$f_i$	$3$	$5$	$6$	$7$

View full solution →

Q 18Solve the Following Question.(4 Marks)4 Marks

The number of telephone calls received at an exchange in 245 successive one- minute intervals are shown in the following frequency distribution:

Number of calls	0	1	2	3	4	5	6	7
Frequency	14	21	25	43	51	40	39	12

Compute the mean deviation about median.

View full solution →

Q 19Solve the Following Question.(4 Marks)4 Marks

Find the mean deviation from the mean for following data:

$x_i$	$5$	$7$	$9$	$10$	$12$	$15$
$f_i$	$8$	$6$	$2$	$2$	$2$	$6$

View full solution →

Q 20Solve the Following Question.(4 Marks)4 Marks

Find the mean deviation from the mean for following data:

$x_i$	$10$	$30$	$50$	$70$	$90$
$f_i$	$4$	$24$	$28$	$16$	$8$

View full solution →

Q 21Solve the Following Question.(5 Marks)5 Marks

Find the coefficient of variation for the following data:

Size (in cms):	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$
No. of items:	$2$	$8$	$20$	$35$	$20$	$15$

View full solution →

Q 22Solve the Following Question.(5 Marks)5 Marks

The mean and standard deviation of 20 observation are found to be 10 and 2 respectively. On reacheking it was found that an observation 8 was incorrect. Calculate the correct and standard deviation in each of the following cases:

If wrong item is omitted.
If it is replaced by 12.

View full solution →

Q 23Solve the Following Question.(5 Marks)5 Marks

Find the standard deviation for the following data:

$x$	$2$	$3$	$4$	$5$	$6$	$7$
$f$	$4$	$9$	$16$	$14$	$11$	$6$

View full solution →

Q 24Solve the Following Question.(5 Marks)5 Marks

Find the numberof observation lying between $\overline{\text{X}}-\text{M.D. }$and $\overline{\text{X}}-\text{M.D. }$ is the mean deviation from the mean.
$34, 66, 30, 38, 44, 50, 40, 60, 42, 51$

View full solution →

Q 25Solve the Following Question.(5 Marks)5 Marks

While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

View full solution →

Statistics question types

Statistics questions

Generate a Statistics paper free

Statistics Maths - Statistics

Statistics question types

Statistics questions

Generate a Statistics paper free