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: $$500 \u003c X \u003c 700$$: 10, $$700 \u003c X \u003c 900$$: 60, $$900 \u003c X \u003c 1500$$: 30. What is the cumulative relative frequency for the class $$900 \u003c X \u003c 1500$$?

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: $$0 \u003c X \u003c 40$$: 13, $$40 \u003c X \u003c 100$$: 21, $$100 \u003c X \u003c 190$$: 8, $$190 \u003c X \u003c 400$$: 8. What is the modal class?

Accepted Answer

$$40 \u003c X \u003c 100$$

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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