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Earn 100

In ten observations, the mean of all $10$ numbers is $15$ , the mean of the first six observations is $16$ and the mean of the last five observations is $12$ . The sixth number is

50% studentsanswered this correctly

Important Questions on Statistics

EASY

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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:

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Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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 and Probability>Statistics>Measures of Central Tendency

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 and Probability>Statistics>Measures of Central Tendency

If the sum of the deviations of

50

observations from

30

50

, then the mean of these observations is :

MEDIUM

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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

MEDIUM

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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 :

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Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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 :

MEDIUM

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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

MEDIUM

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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?

EASY

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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

EASY

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

The average marks of

30

students in a class was

80

. After two students left out of the class, the average marks of the remaining students was

82

. Then the average marks of the two left out students is

HARD

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

In a city, the total income of all people with salary below Rs.

10000

per annum is less than the total income of all people with salary above Rs.

10000

per annum. If the salaries of people in the first group increases by

5 %

and the salaries of people in the second group decreases by

5 %

, then the average income of all people

EASY

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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 and Probability>Statistics>Measures of Central Tendency

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}

HARD

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

Let

x_{1}, x_{2}, \dots, x_{11}

11

distinct positive integers. If we replace the largest of these integers by the median of the other

10

integers, then

MEDIUM

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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 and Probability>Statistics>Measures of Central Tendency

The median of all

4

- digit numbers that are divisible by

7

MEDIUM

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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?

EASY

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

The arithmetic mean of

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

EASY

Mathematics>Statistics and Probability>Statistics>Measures of Central Tendency

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 :

In ten observations, the mean of all 10 numbers is 15, the mean of the first six observations is 16 and the mean of the last five observations is 12. The sixth number is

Important Questions on Statistics

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In ten observations, the mean of all $10$ numbers is $15$ , the mean of the first six observations is $16$ and the mean of the last five observations is $12$ . The sixth number is