Question 1

Which of the following best describes the variable 'Pet Satisfaction' in the household data example?

Accepted Answer

Categorical, ordinal

Question 2

Given the list notation $$\{x_i\}_{i=1}^{n}$$, which of the following is NOT a recommended way to denote a dataset?

Accepted Answer

$$\{x\}_{i=1}^{n}$$

Question 3

Suppose you have a dataset of monthly highest temperatures: $$\{x_1$, x_2$, \ldots, x_{12}\}. $$What is the correct formula to calculate the mean temperature?

Accepted Answer

$$\bar{x} = \frac{1}{12} \sum_{i=1}^{12} x_i$$

Question 4

A sample of household incomes is: $$4200.50, 6100.00, 3900.75, 5000.00, 7200.25. $$What is the mean household income?

Accepted Answer

$$5250.3$$

Question 5

Which of the following statements about the sample variance formula is correct?

Accepted Answer

Sample variance divides by $$n-1 to $$provide an unbiased estimate.

Question 6

Why do we divide by $$n-1$$ instead of $$n$$ when calculating sample variance?

Accepted Answer

To account for the use of the sample mean, which consumes one degree of freedom.

Question 7

Which of the following is a property of summation for constants $$a$$ and $$b$$, and lists $$\{x_i\}$$ and $$\{y_i\}$$?

Accepted Answer

$$\sum_{i=1}^n (a x_i + b y_i) = a \sum_{i=1}^n x_i + b \sum_{i=1}^n y_i$$

Question 8

If a dataset is $$\{2, 4, 6\}$$, what is the sample standard deviation?

Accepted Answer

$$2$$

Question 9

Which of the following is TRUE about the mode?

Accepted Answer

The mode is the value that appears most frequently.

Question 10

Given the dataset $$\{2, 2, 3, 4, 4, 4, 5\}$$, what is the mode?

Accepted Answer

$$4$$

Question 11

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

Accepted Answer

Range

Question 12

If the sample variance of a dataset is $$s^2 = 4$, what is the sample standard deviation?

Accepted Answer

$$2$$

Question 13

Which of the following best explains the concept of 'degrees of freedom' in the context of sample variance?

Accepted Answer

It refers to the number of independent pieces of information after accounting for the sample mean.

Question 14

Which formula correctly expresses the sample variance for a dataset $$\{x_1$, x_2$, \ldots, x_n\}$$?

Accepted Answer

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

Question 15

Which of the following statements is TRUE regarding the calculation of the mean for categorical variables?

Accepted Answer

The mean cannot be calculated for categorical variables.

Question 16

If you have two lists $$\{x_i\}$$ and $$\{y_i\} of $$the same length, which property of summation is correct?

Accepted Answer

$$\sum_{i=1}^n (x_i + y_i) = \sum_{i=1}^n x_i + \sum_{i=1}^n y_i$$

Preliminaries in Applied Statistics: Data Types, Notation, and Descriptive Statistics

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