Question

identify the lower class limits, upper class limits, class width, class midpoints, and class in the summary. age (yr) when award was won frequency 25 - 29 30 30 - 34 33 35 - 39 13 40 - 44 3 45 - 49 4 50 - 54 1 55 - 59 1 5 (type an integer or a decimal. do not round.) identify the class midpoints. 27, 32, 37, 42, 47, 52, 57 (type integers or decimals. do not round. use ascending order.) identify the class boundaries. (type integers or decimals. do not round. use ascending order.)

Explanation:

Step1: Find lower class limits

The lower number in each class - interval is the lower class limit. So, the lower class limits are 25, 30, 35, 40, 45, 50, 55.

Step2: Find upper class limits

The upper number in each class - interval is the upper class limit. So, the upper class limits are 29, 34, 39, 44, 49, 54, 59.

Step3: 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 class 25 - 29 and the second class 30 - 34, the class width is \(30 - 25=5\). Since the class - intervals are uniform, the class width is 5 for all classes.

Step4: Calculate class mid - points

The class mid - point is calculated as \(\frac{\text{lower class limit}+\text{upper class limit}}{2}\). For the class 25 - 29, the mid - point is \(\frac{25 + 29}{2}=27\); for 30 - 34, \(\frac{30+34}{2}=32\); for 35 - 39, \(\frac{35 + 39}{2}=37\); for 40 - 44, \(\frac{40+44}{2}=42\); for 45 - 49, \(\frac{45+49}{2}=47\); for 50 - 54, \(\frac{50+54}{2}=52\); for 55 - 59, \(\frac{55+59}{2}=57\).

Step5: Find class boundaries

To find the lower class boundary, subtract 0.5 from the lower class limit. To find the upper class boundary, add 0.5 to the upper class limit.
For the first class: Lower class boundary \(=25 - 0.5 = 24.5\), upper class boundary \(=29+0.5 = 29.5\).
For the second class: Lower class boundary \(=30 - 0.5 = 29.5\), upper class boundary \(=34 + 0.5=34.5\).
For the third class: Lower class boundary \(=35 - 0.5 = 34.5\), upper class boundary \(=39+0.5 = 39.5\).
For the fourth class: Lower class boundary \(=40 - 0.5 = 39.5\), upper class boundary \(=44+0.5 = 44.5\).
For the fifth class: Lower class boundary \(=45 - 0.5 = 44.5\), upper class boundary \(=49+0.5 = 49.5\).
For the sixth class: Lower class boundary \(=50 - 0.5 = 49.5\), upper class boundary \(=54+0.5 = 54.5\).
For the seventh class: Lower class boundary \(=55 - 0.5 = 54.5\), upper class boundary \(=59+0.5 = 59.5\).
The class boundaries in ascending order are 24.5, 29.5, 34.5, 39.5, 44.5, 49.5, 54.5, 59.5.

Answer:

Lower class limits: 25, 30, 35, 40, 45, 50, 55
Upper class limits: 29, 34, 39, 44, 49, 54, 59
Class width: 5
Class mid - points: 27, 32, 37, 42, 47, 52, 57
Class boundaries: 24.5, 29.5, 34.5, 39.5, 44.5, 49.5, 54.5, 59.5