Q: Which of the following best describes the range $R$ of a variable?

$R = \text{largest data value} - \text{smallest data value}$

Question 1

Which of the following best describes the population mean $\mu$ for a variable $x$ with $N$ observations $x_1, x_2, ..., x_N$?

Accepted Answer

$\mu = \dfrac{\sum_{i=1}^{N} x_i}{N}$

Question 2

Given the data set: 23, 36, 23, 18, 5, 26, 43, what is the median?

Accepted Answer

23

Question 3

Which measure of central tendency is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 4

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

Accepted Answer

Mean > Median

Question 5

For the data set: 23, 36, 23, 18, 5, 26, 43, what is the range?

Accepted Answer

38

Question 6

Which formula correctly calculates the sample standard deviation $s$ for $n$ observations $x_1, x_2, ..., x_n$ with sample mean $\bar{x}$?

Accepted Answer

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

Question 7

A start-up web development company has travel times (in minutes) for its employees: 23, 36, 23, 18, 5, 26, 43. If a new employee with a travel time of 70 minutes is added, what happens to the mean and median?

Accepted Answer

The mean increases more than the median

Question 8

Which of the following is the correct interpretation of the mode?

Accepted Answer

The most frequent observation in the data set

Question 9

Suppose you have a symmetric data set. Which statement is true about the mean and median?

Accepted Answer

Mean equals median

Question 10

Which of the following best describes the range $R$ of a variable?

Accepted Answer

$R = 	ext{largest data value} - 	ext{smallest data value}$

Question 11

If a data set has two values that occur most frequently, what is the mode?

Accepted Answer

The data set is bimodal

Question 12

Which measure of dispersion is calculated as the square root of the average squared deviation from the mean for a population?

Accepted Answer

Population standard deviation

Question 13

Given the following sample: 1.50, 0.79, 1.01, 1.69, 1.72, 2.04, 0.47, 2.53, 1.40, 0.95, 0.90, 1.23, 1.02, 1.09, 1.39, 1.72, 2.04, 1.99, 1.00, 1.35. What is the first step in finding the sample mean?

Accepted Answer

Sum all the values

Question 14

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

Accepted Answer

Range

Question 15

If the sample mean $\bar{x}$ of a data set is 25 and the sample size $n$ is 5, what is the sum of the data values?

Accepted Answer

125

Question 16

Which of the following statements about the mean is true?

Accepted Answer

It is not resistant to outliers

Question 17

A sample of wait times at two restaurants is collected. McDonald's has a mean wait time of 2.5 minutes and Wendy's has a mean wait time of 1.5 minutes. Which restaurant has a higher average wait time?

Accepted Answer

McDonald's

Question 18

Which formula represents the population standard deviation $\sigma$ for $N$ observations $x_1, x_2, ..., x_N$ with mean $\mu$?

Accepted Answer

$\sigma = \sqrt{\dfrac{\sum_{i=1}^{N} (x_i - \mu)^2}{N}}$

Question 19

If a data set is skewed left, which of the following is typically true?

Accepted Answer

Mean < Median

Measures of Central Tendency and Dispersion in Statistics: Study Notes

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