1.3 Frequency, Frequency Tables, and Levels of Measurement
- Page ID
- 36448
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Learning Objective:
In this section, you will:
• Use rounding rules to round final answers.
• Determine the levels of measurement for data.
• Use frequency tables to organize and analyze data.
Answers and Rounding Off
• Carry your final answer one more decimal place than was present in the original data.
• Round off only the final answer. Do not round off any intermediate results, if possible.
Levels of Measurement
Data can be classified into four levels of measurement.
• Nominal scale level: Categories, colors, names, labels, yes or no responses. Nominal scale data are not ordered.
• Ordinal scale level: Data can be ordered, but differences are meaningless.
• Interval scale level: Data can be ordered, but differences are meaningful. Data does not have a starting point.
• Ratio scale level: Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated.
Frequency Tables
• A frequency is the number of times a value of the data occurs.
• A relative frequency is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes.
o To find the relative frequencies, divide each frequency by the total number of students in the sample.
• Cumulative relative frequency is the accumulation of the previous relative frequencies.
o To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row
Example 1:
Complete the frequency table with the following information. Twenty students are asked how many hours they worked per day. Their responses, in hours, are as follows: 5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3.
| Hours Worked per Day | Frequency | Relative Frequency | Cumulative Relative Frequency |
- What percent of students work exactly 4 hours?
- What percent of students that work less than 3 hours?
- What is the percent of students that work from 4 to 6 hours?
- Find the number of students that work from 3 to 5 hours?
- What fraction of the students work from 6 to 7 hours?
- What is the frequency of students that work from 3 to 6 hours?
- What is the relative frequency of students that work 3 or less?
- What is the cumulative relative frequency for 4? Explain what this number tells you about the data.
For more information and examples see online textbook OpenStax Introductory Statistics pages 26-35.
“Introduction to Statistics” by OpenStax, used is licensed under a Creative Commons Attribution License 4.0 license.