Question 1

Which of the following statements best describes the arithmetic mean?

Accepted Answer

It is the sum of all observed values divided by the number of observations.

Question 2

A company tracks the monthly sales (in thousands of dollars) for 12 months: 10, 12, 14, 15, 17, 18, 18, 24, 25, 27, 30, 35. What is the median sales value?

Accepted Answer

$$\frac{18 + 24}{2} = 21$$

Question 3

Which measure of central tendency is most affected by extreme values (outliers)?

Accepted Answer

Arithmetic Mean

Question 4

Given the following house prices: $$2,000,000, 500$$,000, $$300,000, 100$$,000, $100,000, what is the mode?

Accepted Answer

$100,000

Question 5

A data set has a mean of 48.67, a minimum of 43.33, and a maximum of 53.33. What is the range?

Accepted Answer

$$53.33 - 43.33 = 10$$

Question 6

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile and the first quartile: $$IQR = Q_3$ - Q_1$

Question 7

If a distribution is right-skewed, which of the following is most likely true?

Accepted Answer

Mean \u003e Median

Question 8

A sample has a mean $$\bar{X} = 16$$ and a standard deviation $$S = 4. $$What is the z-score for a value $$X = 24$$?

Accepted Answer

$$z = \frac{24 - 16}{4} = 2$$

Question 9

Which formula is used to calculate the sample variance?

Accepted Answer

$$S^2$$ = \frac{1}{n-1} \sum_{i=1}^n (X_i - \bar{X}$$)^2$$

Question 10

A company wants to compare the variability of two stocks. Stock A has a mean price of $$100 and a standard deviation of 10. $$Stock B has a mean price of $$50 and a standard deviation of 10. $$Which stock has a higher coefficient of variation?

Accepted Answer

Stock A: $$CV = \frac{10}{100} = 0.1$$; Stock B: $$CV = \frac{10}{50} = 0.2. $$Stock B has a higher coefficient of variation.

Question 11

According to Chebyshev’s Theorem, at least what percentage of values will fall within 2 standard deviations of the mean for any data set?

Accepted Answer

75%

Question 12

Which of the following is NOT a property of the correlation coefficient $$r$$?

Accepted Answer

It implies causation between variables.

Question 13

A data set has $$Q_1 = 30$, Q_3$ = 57. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = 57 - 30 = 27$$

Question 14

If the mean monthly rent is $$875 with a standard deviation of 219$$, what is the z-score for a rent of $1,325?

Accepted Answer

$$z = \frac{1,325 - 875}{219} \approx 2.05$$

Question 15

Which of the following best describes a box-and-whisker plot?

Accepted Answer

A graphical display of data using the 5-number summary: minimum, $$Q_1$$, median, $$Q_3$$, maximum.

Question 16

Which formula is used to standardize a value $$x$$ from a population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 17

A distribution is described as platykurtic. What does this mean?

Accepted Answer

It has heavier tails and a lower peak than a normal distribution.

Question 18

Which of the following is the correct formula for the sample covariance between $$X$$ and $$Y$$?

Accepted Answer

$$s_{XY} = \frac{1}{n-1} \sum_{i=1}^n (X_i - \bar{X})(Y_i - \bar{Y})$$

Question 19

A data set has a mean of 50 and a standard deviation of 5. According to the Empirical Rule, approximately what percentage of values lie between 45 and 55?

Accepted Answer

68%

Descriptive Statistics: Measures of Center, Variation, and Correlation

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드