The lower upper quartiles are used to define

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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 and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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 and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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}

is

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

The following is the price of Cabbage over 12 months. What is the median price?

Question Image

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

Find the difference of mean and Median value of

5, 8, 2, 6, 9, 15, 12, 18 o f t h e n u m b e r

?

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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 :

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

The arithmetic mean of

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

is

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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:

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

50^{th}

percentile is equal to __________

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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 and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

The mean and median of $7, 5, 5, 2, 7, 6, 5, 3, 7, 6$ is-

1. $5.3$ and $5$

2. $5$ and $5.5$

3. $5$ and $6$

4. $5.3$ and $5.5$

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

The scores obtained by a team in kabaddi series is as follows:

17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

. Find the mean score obtained by the team?

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

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

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

What is the median of the following list of numbers?

$5, 3, 6, 9, 11, 19$ and $1$

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

If the mean of a set of observations

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

is

20

,

then the mean of

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

is

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

The mean of a set of

30

observation is

75

. If each observations is multiplied by non-zero number

λ

and then each of them is decreased by

25

, their mean remains the same. Then,

λ

is equal to :

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

The probable value of mean deviation when

Q_{3} = 40

and

Q_{1} = 15

is

The lower & upper quartiles are used to define

Important Questions on Interpreting Categorical and Quantitative Data

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