Statistics - UP Board (UPMSP) STD 11 Science MATHS Questions

The standard deviation of first 10 natural numbers is:

A
5.5
B
3.87
C
2.97
✓
2.87

Answer: D.

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.

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Q 3M.C.Q (1 Marks)1 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.

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Q 4M.C.Q (1 Marks)1 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.

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Q 5M.C.Q (1 Marks)1 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.

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Q 61 Marks Question1 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 $Var(X).$

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Q 71 Marks Question1 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.

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Q 81 Marks Question1 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 $Y.$

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Q 91 Marks Question1 Mark

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

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Q 101 Marks Question1 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.

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Q 113 Marks Question3 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?

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Q 123 Marks Question3 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?

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Q 133 Marks Question3 Marks

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

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Q 143 Marks Question3 Marks

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

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Q 153 Marks Question3 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?

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Q 165 Marks Questions5 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

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Q 175 Marks Questions5 Marks

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

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

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Q 185 Marks Questions5 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.

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Q 195 Marks Questions5 Marks

Find the mean deviation from the mean for following data:

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

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Q 205 Marks Questions5 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

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