Q: A student’s final grade is calculated as follows: Homework (weight 20%), Midterm (weight 30%), Final Exam (weight 50%). If the student scores 80 on Homework, 70 on the Midterm, and 90 on the Final Exam, what is the weighted mean of the student’s grades?

$$ (0.2 \times 80) + (0.3 \times 70) + (0.5 \times 90) = 81 $$

Q: Which formula is used to calculate the sample correlation coefficient $$r$$ between variables $$x$$ and $$y$$?

$$ r = \frac{\text{Cov}(x, y)}{s_x s_y} $$

Q: A data set of 12 values is sorted in ascending order. To find the 25th percentile, what is the index point formula you should use?

$$ i = \frac{p}{100} \times n $$

Question 1

A real estate analyst is comparing the average home prices in two neighborhoods. Neighborhood A has a mean price of $$350,000 with a standard deviation of 20$$,000, while Neighborhood B has a mean price of $$350,000 with a standard deviation of 60$$,000. What can you conclude about the consistency of home prices in these neighborhoods?

Accepted Answer

Neighborhood A has more consistent home prices than Neighborhood B.

Question 2

Which formula correctly represents the sample variance for a data set with $$n$$ observations and sample mean $$\bar{x}$$?

Accepted Answer

$$ s^2$ = \frac{\sum_{i=1}^n (x_i - \bar{x})^2$}{n-1} $$

Question 3

A company wants to report the typical salary of its employees. The data set contains a few extremely high executive salaries. Which measure of central tendency should the company use to best represent the typical salary?

Accepted Answer

Median

Question 4

Given the following data set representing the number of products sold per day: 5, 7, 7, 8, 10, 12, 15. What is the mode?

Accepted Answer

7

Question 5

A student’s final grade is calculated as follows: Homework (weight 20%), Midterm (weight 30%), Final Exam (weight 50%). If the student scores 80 on Homework, 70 on the Midterm, and 90 on the Final Exam, what is the weighted mean of the student’s grades?

Accepted Answer

$$ (0.2 	imes 80) + (0.3 	imes 70) + (0.5 	imes 90) = 81 $$

Question 6

Which of the following statements about the median is TRUE?

Accepted Answer

The median is the value that divides the data set into two equal halves.

Question 7

A distribution of exam scores is symmetric and bell-shaped. According to the empirical rule, approximately what percentage of scores fall within two standard deviations of the mean?

Accepted Answer

95%

Question 8

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

$$ z = \frac{60 - 50}{5} = 2 $$

Question 9

Which of the following best describes the relationship between the mean, median, and mode in a right-skewed distribution?

Accepted Answer

Mode \u003c Median \u003c Mean

Question 10

A business wants to compare the variability of two different product lines. Which measure should they use to compare the spread of the data if both data sets are measured in the same units?

Accepted Answer

Standard deviation

Question 11

A sample of five donations to a charity are: $$10, 20$$, $$30, 40$$, $100. What is the range of the donations?

Accepted Answer

$$ 100 - 10 = 90 $$

Question 12

Which formula is used to calculate the sample correlation coefficient $$r$$ between variables $$x$$ and $$y$$?

Accepted Answer

$$ r = \frac{	ext{Cov}(x, y)}{s_x s_y} $$

Question 13

A data set of 12 values is sorted in ascending order. To find the 25th percentile, what is the index point formula you should use?

Accepted Answer

$$ i = \frac{p}{100} 	imes n $$

Question 14

Which of the following statements about the interquartile range (IQR) is correct?

Accepted Answer

The IQR is the difference between the third and first quartiles.

Question 15

A company tracks the number of customers per day for 20 days and finds the first quartile is 58, the second quartile is 75, and the third quartile is 84. What is the interquartile range?

Accepted Answer

$$ 84 - 58 = 26 $$

Question 16

If a value in a data set has a z-score of 0, what does this indicate?

Accepted Answer

The value is equal to the mean.

Question 17

Which of the following is NOT a disadvantage of using the mean to summarize data?

Accepted Answer

The mean is difficult to calculate.

Question 18

A business analyst finds that the correlation coefficient between advertising spending and sales revenue is $$r = 0.85. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship between advertising spending and sales revenue.

Descriptive Statistics for Business: Central Tendency, Variability, and Association

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