Constructing a Cumulative Frequency Distribution for Temperature Data

Math Problem Statement

Construct the cumulative frequency distribution for the given data. Daily Low (degreesF) Frequency

35-39 1 40-44 2 45-49 5 50-54 12 55-59 7 60-64 6 65-69 1 Question content area bottom left Part 1 Construct the cumulative frequency distribution. . . . Question content area right Part 1 Daily Low Temperature (degreesF) Cumulative Frequency Less than 40 enter your response here Less than 45 enter your response here Less than 50 enter your response here Less than 55 enter your response here Less than 60 enter your response here Less than 65 enter your response here Less than 70 enter your response here

Solution

To construct the cumulative frequency distribution, we will sum the frequencies as we progress through the data intervals. Here's the process:

Less than 40: This includes the first interval (35–39), where the frequency is 1.
- Cumulative Frequency = 1
Less than 45: This includes both the first and second intervals (35–39 and 40–44). The total frequency is $1 + 2 = 3$ .
- Cumulative Frequency = 3
Less than 50: This includes the first, second, and third intervals (35–39, 40–44, and 45–49). The total frequency is $1 + 2 + 5 = 8$ .
- Cumulative Frequency = 8
Less than 55: This includes the first four intervals (35–39, 40–44, 45–49, and 50–54). The total frequency is $1 + 2 + 5 + 12 = 20$ .
- Cumulative Frequency = 20
Less than 60: This includes the first five intervals (35–39, 40–44, 45–49, 50–54, and 55–59). The total frequency is $1 + 2 + 5 + 12 + 7 = 27$ .
- Cumulative Frequency = 27
Less than 65: This includes the first six intervals (35–39, 40–44, 45–49, 50–54, 55–59, and 60–64). The total frequency is $1 + 2 + 5 + 12 + 7 + 6 = 33$ .
- Cumulative Frequency = 33
Less than 70: This includes all the intervals (35–39, 40–44, 45–49, 50–54, 55–59, 60–64, and 65–69). The total frequency is $1 + 2 + 5 + 12 + 7 + 6 + 1 = 34$ .
- Cumulative Frequency = 34

Final Cumulative Frequency Distribution:

Daily Low Temperature (°F)	Cumulative Frequency
Less than 40	1
Less than 45	3
Less than 50	8
Less than 55	20
Less than 60	27
Less than 65	33
Less than 70	34

Would you like more details on this process?

Here are some related questions for practice:

How do you find relative frequencies from a cumulative frequency distribution?
Can you explain the difference between frequency and cumulative frequency?
What is the total number of observations in this data set?
How would you create a cumulative frequency polygon for this data?
Why is cumulative frequency useful in statistics?

Tip: The cumulative frequency of the last class should always match the total number of data points.

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Math Problem Analysis

Mathematical Concepts

Statistics
Cumulative Frequency Distribution

Formulas

Cumulative frequency = sum of frequencies up to a certain point

Theorems

None

Suitable Grade Level

Grades 6-9

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