Question 1

Which of the following best describes the arithmetic mean of a dataset?

Accepted Answer

It is computed by summing all the individual values and dividing by the number of values.

Question 2

Given a sample with values 4, 8, 6, 10, and 12, what is the sample arithmetic mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{4 + 8 + 6 + 10 + 12}{5} = 8$$

Question 3

In a medical study, the blood pressure readings of 7 patients are: 120, 130, 125, 140, 135, 128, 132. What is the arithmetic mean of these readings?

Accepted Answer

$$\bar{x} = \frac{120 + 130 + 125 + 140 + 135 + 128 + 132}{7} = 130$$

Question 4

Which formula correctly represents the sample arithmetic mean for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 5

A researcher collects the following data: 15, 20, 25, 30, 35. What is the arithmetic mean, and what does it represent in this context?

Accepted Answer

The mean is $$25$$ and it represents the average value of the data collected.

Question 6

If a dataset contains the values 2, 4, 6, 8, and 10, which of the following statements is true about the arithmetic mean?

Accepted Answer

The mean is equal to the median.

Question 7

A company records the number of products sold over five days: 50, 60, 55, 65, 70. What is the arithmetic mean number of products sold per day?

Accepted Answer

$$\bar{x} = \frac{50 + 60 + 55 + 65 + 70}{5} = 60$$

Question 8

Which of the following is NOT a property of the arithmetic mean?

Accepted Answer

It is always one of the values in the dataset.

Question 9

A student calculates the mean of the numbers 3, 7, 11, and 15. If the student mistakenly divides by 3 instead of 4, what mean do they get?

Accepted Answer

$$\bar{x} = \frac{3 + 7 + 11 + 15}{3} = 12$$

Question 10

In a real-world scenario, why might the arithmetic mean not be the best measure of central tendency for a dataset?

Accepted Answer

Because it can be heavily influenced by outliers or extreme values.

Question 11

Suppose the heights (in cm) of five basketball players are: 180, 190, 185, 200, and 195. What is the arithmetic mean height?

Accepted Answer

$$\bar{x} = \frac{180 + 190 + 185 + 200 + 195}{5} = 190$$

Question 12

Which of the following scenarios best illustrates the use of the arithmetic mean in a real-world context?

Accepted Answer

Calculating the average monthly rainfall in a city over a year.

Question 13

If the arithmetic mean of a dataset is 50 and one value is changed from 60 to 80, what happens to the mean?

Accepted Answer

The mean increases.

Question 14

A sample consists of the following values: 5, 10, 15, 20, 25. If the value 25 is replaced with 35, what is the new mean?

Accepted Answer

$$\bar{x} = \frac{5 + 10 + 15 + 20 + 35}{5} = 17$$

Question 15

Which of the following is the correct notation for the sample mean?

Accepted Answer

$$\bar{x}$$

Question 16

A population consists of the values 2, 4, 6, 8, and 10. What is the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{2 + 4 + 6 + 8 + 10}{5} = 6$$

Question 17

In a dataset, the arithmetic mean is often referred to as:

Accepted Answer

The average

Question 18

Which of the following is a limitation of using the arithmetic mean in statistical analysis?

Accepted Answer

It can be distorted by extreme values (outliers).

Measures of Central Tendency: The Arithmetic Mean

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