Construct the cumulative frequency distribution for the given data.
Daily Low ​(degrees​F)
Frequency
 
​35-39
1
​40-44
2
​45-49
5
​50-54
12
​55-59
7
​60-64
6
​65-69
1
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Part 1
Construct the cumulative frequency distribution.
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Part 1
Daily Low Temperature ​(degrees​F)
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


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

1. **Less than 40:** This includes the first interval (35–39), where the frequency is 1.  
   - Cumulative Frequency = 1

2. **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

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

4. **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

5. **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

6. **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

7. **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:
1. How do you find relative frequencies from a cumulative frequency distribution?
2. Can you explain the difference between frequency and cumulative frequency?
3. What is the total number of observations in this data set?
4. How would you create a cumulative frequency polygon for this data?
5. Why is cumulative frequency useful in statistics?

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

Construct the cumulative frequency distribution for the given data.
Daily Low ​(degrees​F)
35-39: 1
40-44: 2
45-49: 5
50-54: 12
55-59: 7
60-64: 6
65-69: 1

Learn how to construct a cumulative frequency distribution for daily low temperatures, with a step-by-step guide through the data set: 35-39°F (1), 40-44°F (2), 45-49°F (5), 50-54°F (12), 55-59°F (7), 60-64°F (6), and 65-69°F (1). Ideal for students in Grades 6-9.

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