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Elementary Statistics Exam

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Elementary Statistics Exam

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1. Guidelines for constructing a frequency distribution from a data set

The 60% is the PARAMETER. It is the numerical description of the total number of governorsstratified sample-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.

2. In January 2013, 60% of the governors of the 50 states in the USA were republicans. What is the Parameter?

-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.stratified sample1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.The 60% is the PARAMETER. It is the numerical description of the total number of governors

3. A company has been rating television programs for more than 60 years. It uses several sampling procedures, but its main one is to track the viewing patterns of 20,000 households. These contain more than 45,000 people and are chosen to form a cross section of the overall population. The households represent various locations, ethnic groups, and income brackets. The data gathered from the sample of 20,000 households are used to draw inferences about the population of all households in the United States.
-What strata are used in the sample?
-Why is it important to have a stratified sample for these ratings?

4. Members of the population are divided into 2 or more subsets, called strata, that share similar characteristics such as age, gender, ethnicity, or even political preference. A sample is then randomly selected from each of the strata.
Ex: chosen at random, 500 rural and 500 urban persons age 65 or older are asked about their health and experience with prescription drugs...___ sampling was used since the population was divided into two strata (urban & rural) and samples were randomly taken from each strata

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.The 60% is the PARAMETER. It is the numerical description of the total number of governorsstratified sample

5. class boundaries

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.the numbers that separate classes without forming gapsThe 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

6. data

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.consists of information coming from observations, counts, measurements, or responses.The 60% is the PARAMETER. It is the numerical description of the total number of governors

7. skewed right
(positively skewed)

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.A frequency distribution is skewed when the 'tail' of the
graph elongates more to one side than to the other. A distribution is skewed right
(positively skewed) when its tail extends to the rightThe 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

8. sample variance

The 60% is the PARAMETER. It is the numerical description of the total number of governors

This is1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

9. a student scored in the 78% percentile on a exam. what does this mean?

Since the student is in the 78th percentile, that means that 78% of the students who took the actuarial exam fall below that score. Therefore, the student scored higher than 78% of the total number of students1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.The 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

10. lower class boundaries

to find this, you subtract 0.5 from each lower limit.1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.The 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

11. Relative frequency

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.frequency f
Relative Frequency = --------------------- = ------
sum of frequencies n-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.The 60% is the PARAMETER. It is the numerical description of the total number of governors

12. empirical rule

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.For data with a symmetric bell shaped distribution, the standard deviation has the following characteristics - -About 68% of data lie within one standard deviation of the mean - about 95% of data lie within two standard deviations of the mean - -about 99.7% of data lie within three standard deviations of the mean-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.The 60% is the PARAMETER. It is the numerical description of the total number of governors

13. Range, variance, standard deviation

14. Using random digit dialing, researchers call 800 people and ask what obstacles keep them from exercising.
what sampling is used and what bias is present?

The 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.Simple random sampling is used, since each number has an equal chance of being dialed, so all samples of 800 phone numbers have an equal chance of being selected.

Bias
-Individuals may refuse to participate in the sample. This may make the sample less representative of the population.
-Individuals may not be available when the researchers are calling. Those individuals that are available may not be representative of the population
-Telephone sampling only includes people who have telephones. People who own telephones may be older or wealthier on average, and may not be representative of the entire population.1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.

15. Questioning students as they leave a university dorm, a researcher asks 351 students about their reading habits. What sampling is this and what potential source of bias is present?

-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.The 60% is the PARAMETER. It is the numerical description of the total number of governors1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.Convenience sampling is used, because students are chosen due to convenience of location

Bias: Because of the personal nature of the question, students may not answer honestly.
-The sample only consists of members of the population that are easy to get. These members may not be representative of the population.

16. population

The 60% is the PARAMETER. It is the numerical description of the total number of governors1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.the collection of ALL outcomes, responses, measurements, or counts that are of interest

17. Chosen at random, 420 customers at a grocery store are contacted and asked their opinions of the service they received. What kind of sampling is this and what potential bias is present?

-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.The 60% is the PARAMETER. It is the numerical description of the total number of governors1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.Simple random sampling is used, since the business is selecting from its customers at random, and all samples of 420 customers have an equal chance of being selected.

Bias: The wording of the question asked to the customers may influence them towards a particular response. The results would not be usable in this case.

18. How is a sample related to a population?

-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.The 60% is the PARAMETER. It is the numerical description of the total number of governorsa sample is a subset of a population1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.

19. Ages of one person per row in a cinema

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.The 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.sample, because the collection of ages of one person per row is a subset of all the ppl in the cinema

20. The method for selecting a systematic sample is to ______________.

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.order a population in some way and then select members of the population at regular intervalsThe 60% is the PARAMETER. It is the numerical description of the total number of governors

21. sampling

is a count or measure of PART of a population and is more commonly used.The 60% is the PARAMETER. It is the numerical description of the total number of governors1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

22. time series

The 60% is the PARAMETER. It is the numerical description of the total number of governors1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.A data set that is composed of quantitative entries taken
at regular intervals over a period of time-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

23. quartiles and percentiles

1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.The 60% is the PARAMETER. It is the numerical description of the total number of governorsQuartiles
are special cases of
percentiles.

Upper Q1
is the 25th percentile,

Upper Q2
is the 50th percentile, and

Upper Q3
is the 75th percentile.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.

24. Inferential Statistics

The 60% is the PARAMETER. It is the numerical description of the total number of governorsis the branch of statistics that involves using a sample to draw conclusions about a population. A basic tool in the study of this is probability.-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.

25. sampling techniques

-simple random sample
-stratified sample
-cluster sample
-systematic sample
-convenience sampleThe 60% is the PARAMETER. It is the numerical description of the total number of governors-The various locations, ethnic groups, and income brackets that are represented is the strata

-Stratified sampling ensures that each segment of the population is represented.1.) Decide on the number of classes (should be between 5-20 to detect patterns easily)
2.) Find the class width by using the formula....

Range H-L
Class Width = ----------------------- = -----------------
number of classes number of classes

3.) Find the class limits *(use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class...then find the upper limit of the first class & make sure they do not overlap. Then find the remaining upper class limits.)*

4.) Make a tally mark for each data entry in the row of the appropriate class

5.) Count the tally marks to find the total frequency, f, for each classs.

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❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know? Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson© 2026 Fatskills.com

All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know?
Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson
© 2026 Fatskills.com