Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Additionally, identify the count of individuals included in the summary. Age (years) when the award was won: 25-34, 35-44, 45-54, 55-64, 65-74, 75-84, 85-94. Frequencies: 29, 34, 16, 3, 5, 1, 2.
Mathematics · College · Thu Feb 04 2021
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To identify the different components of the frequency distribution for the data on the age when an award was won, we need to analyze the provided class intervals (age ranges) and the corresponding frequencies.
1. Lower Class Limits: These are the smallest numbers that can belong to each of the different classes. For this distribution, the lower class limits are 25, 35, 45, 55, 65, 75, and 85, corresponding to the start of each age range.
2. Upper Class Limits: These are the largest numbers that can belong to each of the different classes. The upper class limits here are 34, 44, 54, 64, 74, 84, and 94, which are the ends of each age range.
3. Class Width: The class width is the difference between the lower limit of a class and the lower limit of the next class. It can also be determined by subtracting the lower class limit from the upper class limit of the same class and adding one (since these are whole numbers representing ages). For the first class (25-34), the class width is 34 - 25 + 1 = 10. Since the data is consistently organized, this width is the same across all classes.
4. Class Midpoints: The class midpoint can be found by averaging the upper and lower class limits of a class or, equivalently, by adding the lower class limit to half of the class width. For the first class (25-34), the midpoint is (25 + 34) / 2 = 29.5. This is also the central value of the class.
5. Class Boundaries: These are the values that separate the classes. If the data were continuous, these would be the true boundaries between classes. However, since we are dealing with discrete data (ages), the class boundaries are calculated by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class limit. The class boundaries for the first class are 25 - 0.5 = 24.5 (lower boundary) and 34 + 0.5 = 34.5 (upper boundary).
6. Frequencies: This is the count of individuals that fall within each class interval. The frequencies provided are 29, 34, 16, 3, 5, 1, and 2, respectively, for each age group. The total count of individuals is the sum of these frequencies, which is 29 + 34 + 16 + 3 + 5 + 1 + 2 = 90 individuals.