Statistics Introduction: Quiz Questions and Answers

1. Which of the following definitions is the definition of the MEDIAN?

The MEDIAN is the value that half of the entries are below and half of the entries are above.

The MEDIAN is the value that has the highest frequency.

The MEDIAN is the largest value.

The MEDIAN is the average calculated by adding up all the values and dividing by the number of entries.

The median is a measure of central tendency in a set of data. It is the value that divides the data into two equal halves, where half of the entries are below and half of the entries are above it. Unlike the mean, the median is not affected by extreme values or outliers, making it a good representation of the "typical" value in a dataset.

Explanation

The median is a measure of central tendency in a set of data. It is the value that divides the data into two equal halves, where half of the entries are below and half of the entries are above it. Unlike the mean, the median is not affected by extreme values or outliers, making it a good representation of the "typical" value in a dataset.

2. Which of the following definitions is the definition of the MEAN?

The MEAN is the largest value.

The MEAN is the value that half of the entries are below and half of the entries are above.

The MEAN is the value that has the highest frequency.

The MEAN is the average calculated by adding up all the values and dividing by the number of entries.

The MEAN is the average calculated by adding up all the values and dividing by the number of entries. This definition accurately describes the concept of the mean in statistics. The mean is the sum of all values divided by the total number of values, providing a measure of central tendency that represents the typical value in a dataset. It is calculated by adding up all the values and dividing by the number of entries, making it a useful tool for analyzing data and understanding the overall trend or average value.

Explanation

The MEAN is the average calculated by adding up all the values and dividing by the number of entries. This definition accurately describes the concept of the mean in statistics. The mean is the sum of all values divided by the total number of values, providing a measure of central tendency that represents the typical value in a dataset. It is calculated by adding up all the values and dividing by the number of entries, making it a useful tool for analyzing data and understanding the overall trend or average value.

3. Statistics are useless since you can design an experiment to prove anything you want to prove statistically.

True

False

This statement is false. Statistics are not useless because they provide a systematic and objective way to analyze and interpret data. While it is true that experiments can be designed to support a particular hypothesis, statistical methods help in determining the validity and reliability of the results. They provide tools to assess the probability of obtaining certain outcomes by chance and to make informed decisions based on evidence. Therefore, statistics play a crucial role in scientific research and decision-making processes.

Explanation

This statement is false. Statistics are not useless because they provide a systematic and objective way to analyze and interpret data. While it is true that experiments can be designed to support a particular hypothesis, statistical methods help in determining the validity and reliability of the results. They provide tools to assess the probability of obtaining certain outcomes by chance and to make informed decisions based on evidence. Therefore, statistics play a crucial role in scientific research and decision-making processes.

4. Which of the following definitions is the definition of the MODE?

The MODE is the value that has the highest frequency.

The MODE is the average calculated by adding up all the values and dividing by the number of entries.

The MODE is the largest value.

The MODE is the value that half of the entries are below and half of the entries are above.

The MODE is the value that has the highest frequency, meaning it is the value that appears most frequently in a given set of data. It is not necessarily the average, the largest value, or the value that divides the entries in half. The mode provides insight into the most common or popular value in a dataset.

Explanation

The MODE is the value that has the highest frequency, meaning it is the value that appears most frequently in a given set of data. It is not necessarily the average, the largest value, or the value that divides the entries in half. The mode provides insight into the most common or popular value in a dataset.

5. Gender is categorized as:

Nominal

Ordinal

Interval

Ratio

Gender is categorized as nominal because it is a categorical variable that represents distinct categories or groups. Nominal variables do not have a specific order or numerical value associated with them. In the case of gender, it represents two or more distinct categories (such as male and female) without any inherent order or numerical value. Therefore, it falls under the nominal category.

Explanation

Gender is categorized as nominal because it is a categorical variable that represents distinct categories or groups. Nominal variables do not have a specific order or numerical value associated with them. In the case of gender, it represents two or more distinct categories (such as male and female) without any inherent order or numerical value. Therefore, it falls under the nominal category.

6. You are interested in how stress affects heart rate in humans. Your dependent variable would be the _____.

Interest

Heart rate

Humans

Stress

The dependent variable in this study is heart rate because it is the variable that is being measured and is expected to be influenced by the independent variable, which is stress. The study aims to investigate the impact of stress on heart rate in humans, making heart rate the variable of interest that is expected to change in response to stress.

Explanation

The dependent variable in this study is heart rate because it is the variable that is being measured and is expected to be influenced by the independent variable, which is stress. The study aims to investigate the impact of stress on heart rate in humans, making heart rate the variable of interest that is expected to change in response to stress.

7. You are conducting a study to see whether a new experimental medication will cause bald men to grow hair. You divide your patients into two groups. To one group, you give the medication. To the other group, you give a placebo. In this study, the correct terms for the taking of the drug and the growth of hair are the following.

Both the medication and the hair growth are dependent variables.

Both the medication and the hair growth are independent variables.

The medication is the dependent variable, and the hair growth is the independent variable.

The medication is the independent variable, and the hair growth is the dependent variable.

In this study, the researcher is testing the effects of the experimental medication on hair growth in bald men. The independent variable is the medication because it is being manipulated by the researcher. The researcher is giving the medication to one group and a placebo to the other group. The dependent variable is the hair growth because it is the outcome that is being measured and observed. The researcher wants to see if the medication has any effect on hair growth. Therefore, the medication is the independent variable and the hair growth is the dependent variable.

Explanation

In this study, the researcher is testing the effects of the experimental medication on hair growth in bald men. The independent variable is the medication because it is being manipulated by the researcher. The researcher is giving the medication to one group and a placebo to the other group. The dependent variable is the hair growth because it is the outcome that is being measured and observed. The researcher wants to see if the medication has any effect on hair growth. Therefore, the medication is the independent variable and the hair growth is the dependent variable.

8. Age is classified as:

Nominal data

Ordinal data

Interval data

Ratio data

Age is classified as ratio data because it has a meaningful zero point and the intervals between values are equal. In other words, age can be measured on a continuous scale and has a fixed starting point (zero years old). Additionally, mathematical operations such as addition, subtraction, multiplication, and division can be performed on age values.

Explanation

Age is classified as ratio data because it has a meaningful zero point and the intervals between values are equal. In other words, age can be measured on a continuous scale and has a fixed starting point (zero years old). Additionally, mathematical operations such as addition, subtraction, multiplication, and division can be performed on age values.

9. What is the median of the following set of numbers? {12,8,13,4,7,6,3,3,15}

12

8

7

7.5

The median is the middle value in a set of numbers when the numbers are arranged in order. First, we need to arrange the set of numbers in order from least to greatest:

{3,3,4,6,7,8,12,13,15}

There are 9 numbers in the set. The middle number is the 5th number, which is 7. Therefore, the median of the set is 7.

Explanation

The median is the middle value in a set of numbers when the numbers are arranged in order. First, we need to arrange the set of numbers in order from least to greatest:

{3,3,4,6,7,8,12,13,15}

There are 9 numbers in the set. The middle number is the 5th number, which is 7. Therefore, the median of the set is 7.

10. What are the mode and the mean for the following set of numbers? {4, 9, 8, 2, 16, 4, 4, 8 ,9, 6}

Mean = 7, mode =8

Mean = 7, mode =4

Mean = 6, mode =8

Mean = 8, mode =9

Mean: To find the mean (average), add all the numbers in the set and divide by the total number of values: (4 + 9 + 8 + 2 + 16 + 4 + 4 + 8 + 9 + 6) / 10 = 70 / 10 = 7

Mode: The mode is the value that appears most frequently in the set. In this case, the number 4 appears three times, which is more than any other number. Sources and related content

Explanation

Mean: To find the mean (average), add all the numbers in the set and divide by the total number of values: (4 + 9 + 8 + 2 + 16 + 4 + 4 + 8 + 9 + 6) / 10 = 70 / 10 = 7

Mode: The mode is the value that appears most frequently in the set. In this case, the number 4 appears three times, which is more than any other number. Sources and related content

Statistics Introduction: Quiz Questions And Answers