Let n ≥ 3 . A list of numbers 0 < x 1 < x 2 < … < x n has mean μ and standard deviation σ . A new list of numbers is made as follows: y 1 = 0 , y 2 = x 2 , … . , y n - 1 = x n - 1 , y n = x 1 + x n . The mean and the standard deviation of the new list are μ ^ & σ ^ . Which of the following is necessarily true?

μ may or may not be equal to μ ^

The quartile deviation of a normal distribution with mean10 and standard deviation4 is

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The standard deviation of a variable

x

is

10

. Then the standard deviation of

50 + 5 x

is

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

If the mean and the standard deviation of the data

3, 5, 7, a, b

are

5

and

2

respectively, then

a

and

b

are the roots of the equation:

HARD

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The standard deviations of

x_{i} (i = 1, 2, \dots . 10)

and

y_{i} (i = 1, \dots 10)

are respectively

a

and

b

.

\bar{x}, \bar{y}

are the means of these two sets of observations respectively. If

z_{i} = (x_{i} - \bar{x}) (y_{i} - \bar{y})

and

\sum_{i = 1}^{10} z_{i} = c

, then the standard deviation of the observations

(x_{i} - y_{i}), (i = 1, 2, \dots 10)

is

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Let

X_{1}, X_{2}, \dots, X_{18}

be eighteen observations such that

\sum_{i = 1}^{18} (X_{i} - α) = 36

and

\sum_{i = 1}^{18} {(X_{i} - β)}^{2} = 90

, where

α

and

β

are distinct real numbers. If the standard deviation of these observations is

1

, then the value of

|α - β|

is _______.

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

For a certain type of mobiles, the length of time between charges of the battery is normally distributed with a mean of

50

hours and a standard deviation of

15

hours. A person owns one of these mobiles and wants to know the probability that the length of time will be between

50

and

70

hours is (Given

ϕ (1.33) = 0.9082, ϕ (0) = 0.5

)

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

In a series of observations half of them equal to

a

and remaining half equal to

- a

. If the S.D. of the observations is

2

, then

| a | =

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

For a group of

100

students, the mean

{\bar{x}}_{1}

and the standard deviation

σ_{1}

of their marks were found to be

40

and

15

respectively. Later it was observed that the scores

40

and

50

were misread as

30

and

60

respectively. If the mean and the standard deviation with the corrected observations of the scores are

{\bar{x}}_{2}

and

σ_{2}

respectively, then

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The standard deviation of

1

to

9

natural numbers is ____________

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Which of the following is not true regarding the normal distribution?

HARD

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Let

n \geq 3

. A list of numbers

0 < x_{1} < x_{2} < \dots < x_{n}

has mean

μ

and standard deviation

σ

. A new list of numbers is made as follows:

y_{1} = 0, y_{2} = x_{2}, \dots ., y_{n - 1} = x_{n - 1}, y_{n} = x_{1} + x_{n}

. The mean and the standard deviation of the new list are

\hat{μ} & \hat{σ}

. Which of the following is necessarily true?

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The Standard Deviation of the numbers

31, 32, 33 \dots \dots . 46, 47

is

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Area covered normal curve by

(μ \pm 3 σ)

is ______.

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Standard deviation of a collection of data is $2 \sqrt{2}$ . If each value is multiplied by $3$ , then the standard deviation of the new data is:

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The S.D of

4, 5, 6, 7, \dots . ., 13

is

x

, then the S.D of

14, 15, \dots \dots 23

is

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Draw the necessary table to find the Standard Deviation for the data $20, 14, 16, 30, 21$ and $25$ .

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The mean and variance of

10

observations were calculated as

15

and

15

respectively by a student who took by mistake

25

instead of

15

for one observation. Then, the correct standard deviation is _______.

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

Find

SD

of

1, 2, 3, 4, 5, 6, 7, 8, 9

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

The standard deviation of the set $(10, 10, 10, 10, 10)$ is

MEDIUM

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

In normal distribution what is the ratio of

QD : MD : SD

?

EASY

Mathematics>Statistics and Probability>Interpreting Categorical and Quantitative Data>Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve

If we change the parameter (s) of a ________ distribution the Sharpe of probability curve does not change.

The quartile deviation of a normal distribution with mean $10$ and standard deviation $4$ is __________

Important Questions on Interpreting Categorical and Quantitative Data

Learn and Prepare for any exam you want !

The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is __________

Important Questions on Interpreting Categorical and Quantitative Data

Learn and Prepare for any exam you want !

The quartile deviation of a normal distribution with mean $10$ and standard deviation $4$ is __________