EASY

Earn 100

Find the mean for the given frequency distribution table.

Class interval Frequency $(f)$

$2 - 4$ $2$

$4 - 6$ $3$

$6 - 8$ $6$

$8 - 10$ $2$

$10 - 12$ $1$

Important Questions on Measures of Central Tendency

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The mean and the median of the following ten numbers in increasing order

10, 22, 26, 29, 34, x, 42, 67, 70, y

are

42

and

35

respectively, then

\frac{y}{x}

is equal to:

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The mean of a data set comprising of $16$ observations is $16$ . If one of the observation value $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data is

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The mean of

n i t e m s i s \bar{X} .

If the first is increased by 1, second by

2

and so on, then the new mean is

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The arithmetic mean of a set of observation is

\bar{X}

. If each observation is divided by

α

and increased by

10

, then the mean of the new series is

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The average incomes of the people in two villages are

P

and

Q

, respectively. Assume that

P \neq Q

. A person moves from the first village to the second village. The new average incomes are

P'

and

Q'

, respectively. Which of the following is not possible?

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

If for some $x \in R$ , the frequency distribution of the marks obtained by $20$ students in a test is:

Marks	2	3	5	7
Frequency distribution	${(x + 1)}^{2}$	$(2 x - 5)$	$x^{2} - 3 x$	$x$

Then the mean of the marks is :

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

In a set of

2 n

distinct observations, each of the observation below the median of all the observations is increased by

5

and each of the remaining observations is decreased by

3

. Then, the mean of the new set of observations :

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The average age of

20

students in a class is

15 years

. If the teacher's age is included, the average increases by one. What is the teacher's age?

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

If the sum of the deviations of

50

observations from

30

50

, then the mean of these observations is :

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The mean age of

25

teachers in a school is

40

years. A teacher retires at the age of

60

years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is

39

years, then the age (in years) of the newly appointed teacher is

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

100

mark examination was administered to a class of

50

students. Despite only integer marks being given, the average score of the class was

47.5

. Then, the maximum number of students who could get marks more than the class average is

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The arithmetic mean of

{}^{n}{C_{0}}, {}^{n}{C_{1}, {}^{n}{C_{2}}} \dots, {}^{n}{C_{n}}

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

If the mean of a set of observations

x_{1}, x_{2}, \dots, x_{10}

20,

then the mean of

x_{1} + 4, x_{2} + 8, x_{3} + 12

\dots \dots, x_{10} + 40

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

If both the mean and the standard deviation of

50

observations

x_{1}, x_{2}, \dots, x_{50}

are equal to

16

, then the mean of

{(x_{1} - 4)}^{2}, {(x_{2} - 4)}^{2}, \dots, {(x_{50} - 4)}^{2}

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

Ram obtained

60

and

85

in the first two unit tests. The minimum marks he should get in the third test to have an average of atleast

55

marks is

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The average weight of a class of

14

students is

42 kg .

On including the teacher the average increases by

400 g,

then weight of teacher is

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

The mean age of

25

teachers in a school is

40

years. A teacher retires at the age of

60

years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is

39

years, then the age (in years) of the newly appointed teacher is

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

Let

n \geq 3 .

A list of numbers

x_{1}, x_{2}, \dots . ., x_{n}

has mean

μ

and standard deviation

σ .

A new list of numbers

y_{1}, y_{2}, \dots . ., y_{n}

is made as follows:

y_{1} = \frac{x_{1} + x_{2}}{2}, y_{2} = \frac{x_{1} + x_{2}}{2} a n d y_{j} = x_{j} f o r j = 3, 4, \dots, n .

The mean and the standard deviation of the new list are

\hat{μ} a n d \hat{σ} .

Then which of the following is necessarily true?

MEDIUM

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

If the mean of a set of observations

x_{1}, x_{2}, \dots x_{10}

20

,

then the mean of

x_{1} + 4, x_{2} + 8, x_{3} + 12, \dots x_{10} + 40

EASY

Mathematics>Statistics>Measures of Central Tendency>Methods to Find Arithmetic Mean for Different Data

A factory is operating in two shifts, day and night, with

70

and

30

workers, respectively.If per day mean wage of the day shift workers is,

₹ 54

and per day mean wage of all the workers is

₹ 60

, then per day mean wage of the night shift workers (in

₹

) is :

Class interval	Frequency $(f)$
$2 - 4$	$2$
$4 - 6$	$3$
$6 - 8$	$6$
$8 - 10$	$2$
$10 - 12$	$1$

Find the mean for the given frequency distribution table. Class interval Frequencyf 2-4 2 4-6 3 6-8 6 8-10 2 10-12 1

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

Find the mean for the given frequency distribution table.

Class interval Frequency $(f)$

$2 - 4$ $2$

$4 - 6$ $3$

$6 - 8$ $6$

$8 - 10$ $2$

$10 - 12$ $1$