Question

use the given information about the data set and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 10, range = 111, 8 classes the class width is 14 (type a whole number) the lower class limits are (type whole numbers. use a comma to separate answers as needed.)

Explanation:

Step1: Calculate class width

Class width \(w=\frac{\text{Range}}{\text{Number of classes}}\). Given range \( = 111\) and number of classes \(n = 8\). \(w=\frac{111}{8}=13.875\). Since class width is a whole - number, we round up to \(w = 14\) (already given).

Step2: Find lower class limits

The first lower class limit \(L_1=\text{min}=10\).
The second lower class limit \(L_2=L_1 + w=10 + 14=24\).
The third lower class limit \(L_3=L_2 + w=24+14 = 38\).
The fourth lower class limit \(L_4=L_3 + w=38 + 14=52\).
The fifth lower class limit \(L_5=L_4 + w=52+14 = 66\).
The sixth lower class limit \(L_6=L_5 + w=66 + 14=80\).
The seventh lower class limit \(L_7=L_6 + w=80+14 = 94\).
The eighth lower class limit \(L_8=L_7 + w=94 + 14=108\).

Step3: Find upper class limits

The first upper class limit \(U_1=L_2 - 1=24 - 1=23\).
The second upper class limit \(U_2=L_3 - 1=38 - 1=37\).
The third upper class limit \(U_3=L_4 - 1=52 - 1=51\).
The fourth upper class limit \(U_4=L_5 - 1=66 - 1=65\).
The fifth upper class limit \(U_5=L_6 - 1=80 - 1=79\).
The sixth upper class limit \(U_6=L_7 - 1=94 - 1=93\).
The seventh upper class limit \(U_7=L_8 - 1=108 - 1=107\).
The eighth upper class limit \(U_8=U_7+w=107 + 14=121\) (since the range is \(111\) and \(\text{min}=10\), \(\text{max}=\text{min}+\text{range}=10 + 111=121\)).

Answer:

The lower class limits are \(10,24,38,52,66,80,94,108\).
The upper class limits are \(23,37,51,65,79,93,107,121\).