Statistics - CBSE STD 11 Science Maths Questions

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

Consider the first $10$ positive integers. If we multiply each number by $-1$ and then add $1$ to each number, the variance of the numbers so obtained is:

✓
$8.25$
B
$6.5$
C
$3.87$
D
$2.87$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark

Let $\ce{a, b, c, d, e}$ be the observations with mean $m$ and standard deviation $s.$ The standard deviation of the observations $\ce{a + k, b + k, c + k, d + k, e + k}$ 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

The standard deviation of some temperature data in $^\circ C$ is $5.$ If the data were converted into $^\circ F,$ the variance would be:

✓
$81$
B
$57$
C
$36$
D
$25$

Answer: A.

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

The following information relates to a sample of size $60 \sum\text{x}^2=18000$ and $\sum\text{x}=960,$ then the variance is:

A
$6.63$
B
$16$
C
$22$
✓
$44$

Answer: D.

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

Mean deviation for n observations $x_1, x_2, ...... , x_n$ from their mean $x$ is given by:

A
$\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})$
✓
$\frac{1}{\text{n}}\sum\limits^{\text{n}}_{\text{i}=1}|\text{x}_\text{i}-\bar{\text{x}}|$
C
$\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})^2$
D
$\frac{1}{\text{n}}\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})^2$

Answer: B.

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Q 63 Marks Question3 Marks

For the frequency distribution:

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

Find the standard distribution.

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Q 73 Marks Question3 Marks

Find the mean and variance of the frequency distribution given below:

$\text{x}$	$1\leq\text{x}<3$	$3\leq\text{x}<5$	$5\leq\text{x}<7$	$7\leq\text{x}<10$
$\text{f}$	$6$	$4$	$5$	$1$

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Q 83 Marks Question3 Marks

If for a distribution $\sum(\text{x}-5)=3,\sum(\text{x}-5)^2=43$ and the total number of item is 18, find the mean and standard deviation.

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Q 93 Marks Question3 Marks

Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.

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Q 103 Marks Question3 Marks

Mean and standard deviation of 100 items are 50 and 4, respectively. Find the sum of all the item and the sum of the squares of the items.

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Q 11Fill In The Blanks[1 Marks ]1 Mark

If the variance of a data is 121, then the standard deviation of the data is _______.

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Q 12Fill In The Blanks[1 Marks ]1 Mark

The sum of the squares of the deviations of the values of the variable is _______ when taken about their arithmetic mean.

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Q 13Fill In The Blanks[1 Marks ]1 Mark

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 $\sum(\text{x}_\text{i}-\text{a})^2$

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Q 14Fill In The Blanks[1 Marks ]1 Mark

The standard deviation is _________ to the mean deviation taken from the arithmetic mean.

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Q 15Fill In The Blanks[1 Marks ]1 Mark

$\text{Cofficient of variation}=\frac{......}{\text{Mean}}\times100$

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Q 165 Marks Questions5 Marks

Following are the marks obtained$,$ out of $100, $by two students Ravi and Hashina in $10$ tests.

Ravi	$25$	$50$	$45$	$30$	$72$	$42$	$36$	$48$	$35$	$60$
Hashima	$10$	$70$	$50$	$20$	$95$	$55$	$42$	$60$	$48$	$80$

Who is more intelligent and who is more consistent?

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Q 175 Marks Questions5 Marks

Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

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Q 185 Marks Questions5 Marks

The frequency distribution:

$x$	$A$	$2A$	$3A$	$4A$	$5A$	$6A$
$f$	$2$	$1$	$1$	$1$	$1$	$1$

where $A$ is a positive integer$,$ has a variance of $160.$ Determine the value of $A.$

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Q 195 Marks Questions5 Marks

Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number.

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Q 205 Marks Questions5 Marks

Calculate the mean deviation about the mean for the following frequency distribution:

Class interval	$0-4$	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$4$	$6$	$8$	$5$	$2$

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