Question 1

Which of the following statements best describes the mean as a measure of central tendency?

Accepted Answer

The mean is calculated by summing all data values and dividing by the number of observations.

Question 2

Given the following sample data: 10, 15, 20, 25, 100, which measure of central tendency would be LEAST affected by the outlier (100)?

Accepted Answer

Median

Question 3

A company wants to calculate the average number of products sold per day over a week, but some days are more important than others. Which formula should they use?

Accepted Answer

$\bar{X} = \frac{\sum_{i=1}^n (w_i x_i)}{\sum_{i=1}^n w_i}$

Question 4

Which of the following is a disadvantage of using the range as a measure of variability?

Accepted Answer

It only considers the two most extreme values and ignores the rest of the data.

Question 5

A sample of exam scores is: 70, 75, 80, 85, 90. What is the sample mean?

Accepted Answer

$\bar{X} = 80$

Question 6

If a data set is right-skewed, which of the following is true about the relationship between the mean and the median?

Accepted Answer

Mean > Median

Question 7

Which formula would you use to calculate the sample standard deviation?

Accepted Answer

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

Question 8

A company has two products. Product A has a mean sales of 100 units with a standard deviation of 5. Product B has a mean sales of 200 units with a standard deviation of 20. Which product has more relative variability?

Accepted Answer

Product B, because its coefficient of variation is higher.

Question 9

What is the z-score for a value of 85 in a sample with mean 80 and standard deviation 5?

Accepted Answer

$z = 1$

Question 10

According to the empirical rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 11

Chebyshev’s Theorem states that for any data set, at least what percentage of values fall within 3 standard deviations of the mean?

Accepted Answer

89%

Question 12

A grouped frequency table has class midpoints of 5, 15, and 25 with frequencies 2, 3, and 5, respectively. What is the sample mean?

Accepted Answer

$\bar{X} = 17$

Question 13

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

Accepted Answer

The difference between the third quartile and the first quartile.

Question 14

If a data set has a minimum of 10, Q1 = 20, median = 30, Q3 = 40, and maximum = 100, what is the five-number summary?

Accepted Answer

10, 20, 30, 40, 100

Question 15

A sample has a mean of 50 and a standard deviation of 10. What is the coefficient of variation (CV) for this sample?

Accepted Answer

$CV = 20\%$

Question 16

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

Accepted Answer

$r = \frac{s_{xy}}{s_x s_y}$

Question 17

If the sample correlation coefficient $r$ between two variables is -0.95, what does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 18

A data set has 20 values. What is the index point for the 75th percentile?

Accepted Answer

$i = 0.75 	imes 20 = 15$

Question 19

A value in a data set has a z-score of 2.5. What does this mean?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Descriptive Statistics: Measures of Central Tendency and Variability

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