Question

identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. also identify the number of individuals included in the summary. age (yr) when award was won frequency 25 - 34 31 35 - 44 32 45 - 54 15 55 - 64 2 65 - 74 4 75 - 84 1 85 - 94 1 identify the lower class limits 25 35 45 55 65 75 85 (type integers or decimals. do not round. use ascending order.) identify the upper class limits (type integers or decimals. do not round. use ascending order.)

Explanation:

Step1: Identify upper class limits

The upper value of each class interval is the upper class limit. For the intervals 25 - 34, 35 - 44, 45 - 54, 55 - 64, 65 - 74, 75 - 84, 85 - 94, the upper class limits are 34, 44, 54, 64, 74, 84, 94 respectively.

Step2: Calculate class width

The class width is found by subtracting the lower limit of a class from the lower limit of the next - class. For example, for the first two classes 25 - 34 and 35 - 44, class width = 35 - 25=10. Since the intervals are uniform, the class width is 10 for all classes.

Step3: Calculate class mid - points

The class mid - point is calculated as $\frac{\text{lower class limit}+\text{upper class limit}}{2}$. For the first class 25 - 34, mid - point=$\frac{25 + 34}{2}=29.5$. For 35 - 44, mid - point=$\frac{35+44}{2}=39.5$, for 45 - 54, mid - point=$\frac{45 + 54}{2}=49.5$, for 55 - 64, mid - point=$\frac{55+64}{2}=59.5$, for 65 - 74, mid - point=$\frac{65 + 74}{2}=69.5$, for 75 - 84, mid - point=$\frac{75+84}{2}=79.5$, for 85 - 94, mid - point=$\frac{85 + 94}{2}=89.5$.

Step4: Calculate class boundaries

The lower class boundary of a class is found by subtracting 0.5 from the lower class limit and the upper class boundary is found by adding 0.5 to the upper class limit. For the first class 25 - 34, lower class boundary = 24.5 and upper class boundary = 34.5. For 35 - 44, lower class boundary = 34.5 and upper class boundary = 44.5, and so on.

Step5: Calculate number of individuals

The number of individuals is the sum of the frequencies. $31+32 + 15+2+4+1+1=86$.

Answer:

• Upper class limits: 34, 44, 54, 64, 74, 84, 94
• Class width: 10
• Class mid - points: 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5
• Class boundaries: 24.5 - 34.5, 34.5 - 44.5, 44.5 - 54.5, 54.5 - 64.5, 64.5 - 74.5, 74.5 - 84.5, 84.5 - 94.5
• Number of individuals: 86