Q: Given a grouped frequency distribution, which formula is used to estimate the mean?

$\overline{x} = \frac{\sum f_i x_i}{\sum f_i}$

Q: Which of the following best describes the range of a data set?

The difference between the highest and lowest values.

Q: Which of the following is the correct formula for the variance of a sample?

$s^2 = \frac{\sum (x_i - \overline{x})^2}{n-1}$

Q: If 50% of a data set is above the mode, which of the following must be true?

Nothing can be concluded about the distribution.

Q: Which of the following is a correct interpretation of a cumulative frequency distribution?

It shows the total number of observations up to and including each class.

Q: If the sum of frequencies in a grouped frequency distribution is $n$, and the sum of the products of class midpoints and frequencies is $\sum f_i x_i$, what is the formula for the mean?

$\overline{x} = \frac{\sum f_i x_i}{n}$

Question 1

Which of the following statements about the median is correct?

Accepted Answer

The median is a measure of central tendency that is not affected by extreme values.

Question 2

Given a data set $x_1, x_2, ..., x_n$ with mean $\overline{x}$, which of the following is always true?

Accepted Answer

$\sum_{i=1}^n (x_i - \overline{x}) = 0$

Question 3

Which of the following best describes a continuous variable?

Accepted Answer

A variable that can take any value within a given range.

Question 4

Quartiles are used to:

Accepted Answer

Divide a data set into four equal parts.

Question 5

A sample of 25 municipal employees has the following income class frequencies: 4, 4, 10, 5, 2. What is the mean annual salary if the class midpoints are $20,000$, $30,000$, $40,000$, $50,000$, and $60,000$ respectively?

Accepted Answer

$\$37,000$

Question 6

If the mean salary of public servants is $\$30,000$ and municipal employees earn 30% more, what is the mean salary of municipal employees?

Accepted Answer

$\$39,000$

Question 7

Given the following frequency distribution of fish lengths (in mm): 275-300: 1, 300-325: 14, 325-350: 24, 350-375: 26, 375-400: 20, 400-425: 10, 425-450: 2, 450-475: 2, what is the modal class?

Accepted Answer

350-375

Question 8

A sample of 100 families has the following expenditure distribution: $500 < X < 700$: 10, $700 < X < 900$: 60, $900 < X < 1500$: 30. What is the cumulative relative frequency for the class $900 < X < 1500$?

Accepted Answer

$1.00$

Question 9

Given a grouped frequency distribution, which formula is used to estimate the mean?

Accepted Answer

$\overline{x} = \frac{\sum f_i x_i}{\sum f_i}$

Question 10

If a data set has a mean of $12.68$ and the sum of squared deviations from the mean is $320$, what is the standard deviation for a sample size of $50$?

Accepted Answer

$2.55$

Question 11

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 12

A survey of 50 students found the following expenditure distribution: $0 < X < 40$: 13, $40 < X < 100$: 21, $100 < X < 190$: 8, $190 < X < 400$: 8. What is the modal class?

Accepted Answer

$40 < X < 100$

Question 13

Which of the following best describes the range of a data set?

Accepted Answer

The difference between the highest and lowest values.

Question 14

In a frequency distribution, the class interval with the highest frequency is called:

Accepted Answer

The modal class

Question 15

If the cumulative relative frequency for the class $[170, 180[$ is $0.6$ in a sample of 200 athletes, how many athletes are shorter than $180$ cm?

Accepted Answer

$120$

Question 16

Which of the following is the correct formula for the variance of a sample?

Accepted Answer

$s^2 = \frac{\sum (x_i - \overline{x})^2}{n-1}$

Question 17

A data set has the following values: 2, 4, 4, 5, 7, 8, 9. What is the median?

Accepted Answer

5

Question 18

If 50% of a data set is above the mode, which of the following must be true?

Accepted Answer

Nothing can be concluded about the distribution.

Question 19

Which of the following is a correct interpretation of a cumulative frequency distribution?

Accepted Answer

It shows the total number of observations up to and including each class.

Question 20

If the sum of frequencies in a grouped frequency distribution is $n$, and the sum of the products of class midpoints and frequencies is $\sum f_i x_i$, what is the formula for the mean?

Accepted Answer

$\overline{x} = \frac{\sum f_i x_i}{n}$

Statistics for Business: Key Concepts, Calculations, and Applications

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