Math Problem Statement
Solution
To solve this problem, we need to:
- Group the temperatures into the given intervals.
- Calculate the relative frequency for each group by dividing the number of data points in each group by the total number of data points (17).
- Express the result as a decimal rounded to the nearest hundredth.
The intervals provided are:
- 93 to 96
- 97 to 100
- 101 to 104
- 105 to 108
- 109 to 112
Step 1: Organize the data into intervals
The temperatures given are: 108, 104, 101, 112, 109, 110, 99, 106, 102, 105, 94, 94, 107, 93, 103, 105, 103.
Now, we count how many temperatures fall within each range:
- 93 to 96: 93, 94, 94 → 3 temperatures
- 97 to 100: 99 → 1 temperature
- 101 to 104: 101, 102, 103, 103, 104 → 5 temperatures
- 105 to 108: 105, 105, 106, 107, 108 → 5 temperatures
- 109 to 112: 109, 110, 112 → 3 temperatures
Step 2: Calculate the relative frequency
To find the relative frequency for each group, divide the count for each interval by the total number of data points (17). Then, round to the nearest hundredth.
- 93 to 96:
- 97 to 100:
- 101 to 104:
- 105 to 108:
- 109 to 112:
Final table:
Temperature (in °C) | Relative frequency |
---|---|
93 to 96 | 0.18 |
97 to 100 | 0.06 |
101 to 104 | 0.29 |
105 to 108 | 0.29 |
109 to 112 | 0.18 |
Would you like more details on any step, or do you have any questions?
Here are five related questions for further exploration:
- What is the total frequency for all the groups?
- How would the frequencies change if the class width was increased to 5?
- What does the sum of all the relative frequencies represent?
- How can we create a cumulative frequency distribution from this data?
- How would the relative frequency distribution change with more data points?
Tip: Always ensure that the sum of relative frequencies equals approximately 1 when rounded to the nearest hundredth.
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Math Problem Analysis
Mathematical Concepts
Statistics
Grouped Data
Relative Frequency
Formulas
Relative Frequency = (Frequency of class) / (Total number of data points)
Theorems
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Suitable Grade Level
High School (Grades 9-12)
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