1. **Problem Statement:** Prepare a frequency distribution table for the given data sets with specified class intervals. 2. **Frequency Distribution Table Construction:** - Frequency distribution groups data into classes and counts the number of data points in each class. - Class intervals must be mutually exclusive and exhaustive. - Frequency is the count of data points in each class. - Mid-value (class mark) is the midpoint of each class interval. - Class boundaries separate classes without gaps. 3. **Example: Frequency Distribution for Data with Class Intervals 10-19, 20-29, ...** - Data: 40 28 15 28 27 25 26 39 40 37 39 41 28 36 55 32 57 32 41 10 45 59 51 28 43 37 33 28 42 39 31 39 18 36 45 37 26 23 42 58 37 36 33 20 23 42 28 37 44 36 40 39 41 39 38 38 16 41 27 19 - Classes: 10-19, 20-29, 30-39, 40-49, 50-59 - Count frequencies: - 10-19: 15, 10, 18, 16, 19 (5) - 20-29: 28, 28, 27, 25, 26, 28, 28, 23, 23, 27 (10) - 30-39: 32, 32, 33, 33, 36, 36, 36, 37, 37, 37, 37, 38, 38, 39, 39, 39, 39, 39, 40, 40, 40, 41, 41, 41, 41, 42, 42, 42, 43, 44 (30) - 40-49: 40, 41, 42, 43, 44 (5) - 50-59: 51, 55, 57, 58, 59 (5) 4. **Frequency Distribution Table:** | Class Interval | Frequency | | 10 - 19 | 5 | | 20 - 29 | 10 | | 30 - 39 | 30 | | 40 - 49 | 5 | | 50 - 59 | 5 | 5. **Mid-values:** Mid-value = $\frac{\text{Lower limit} + \text{Upper limit}}{2}$ - For 10-19: $\frac{10+19}{2} = 14.5$ - For 20-29: $24.5$ - For 30-39: $34.5$ - For 40-49: $44.5$ - For 50-59: $54.5$ 6. **Class Boundaries:** - Lower boundary of first class = Lower limit - 0.5 = 9.5 - Upper boundary of first class = Upper limit + 0.5 = 19.5 - Similarly for others: 19.5-29.5, 29.5-39.5, 39.5-49.5, 49.5-59.5 7. **Summary:** Frequency distribution helps summarize data for analysis. --- **Slug:** frequency-distribution **Subject:** statistics **Desmos:** {"latex":"","features":{"intercepts":true,"extrema":true}} **q_count:** 1