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 lower class limits

Given directly as 25, 35, 45, 55, 65, 75, 85.

Step2: Identify upper class limits

The upper class limits for the intervals 25 - 34, 35 - 44, 45 - 54, 55 - 64, 65 - 74, 75 - 84, 85 - 94 are 34, 44, 54, 64, 74, 84, 94.

Step3: Calculate class width

Take the first - class interval 25 - 34. Class width = upper limit - lower limit = 34 - 25+1 = 10. Since it's a uniform - width distribution, the class width for all intervals is 10.

Step4: Calculate class midpoints

For a class interval \(a - b\), the mid - point \(M=\frac{a + b}{2}\). For 25 - 34, \(M=\frac{25+34}{2}=29.5\). For 35 - 44, \(M=\frac{35 + 44}{2}=39.5\). For 45 - 54, \(M=\frac{45+54}{2}=49.5\). For 55 - 64, \(M=\frac{55+64}{2}=59.5\). For 65 - 74, \(M=\frac{65+74}{2}=69.5\). For 75 - 84, \(M=\frac{75+84}{2}=79.5\). For 85 - 94, \(M=\frac{85+94}{2}=89.5\).

Step5: 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 boundary = 24.5 and upper boundary = 34.5. For 35 - 44, lower boundary = 34.5 and upper boundary = 44.5. For 45 - 54, lower boundary = 44.5 and upper boundary = 54.5. For 55 - 64, lower boundary = 54.5 and upper boundary = 64.5. For 65 - 74, lower boundary = 64.5 and upper boundary = 74.5. For 75 - 84, lower boundary = 74.5 and upper boundary = 84.5. For 85 - 94, lower boundary = 84.5 and upper boundary = 94.5.

Step6: Calculate number of individuals

Sum the frequencies: \(31+32 + 15+2+4+1+1=86\).

Answer:

Lower class limits: 25, 35, 45, 55, 65, 75, 85
Upper class limits: 34, 44, 54, 64, 74, 84, 94
Class width: 10
Class midpoints: 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5
Class boundaries: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5
Number of individuals: 86