Question

1. the number of students per teacher at a high school ranges from 7 to 26 students. find the class width and then find the class limits if the data were to be separated into five classes.

error analysis - state the reason why each frequency table below is incorrectly constructed.

1. class limit frequency

27 - 32 1
33 - 38 0
39 - 44 6
45 - 49 4
50 - 55 2

1. class limit frequency

5 - 9 1
9 - 13 2
13 - 17 5
17 - 20 6
20 - 24 3

1. class limit frequency

123 - 127 3
128 - 132 7
138 - 142 2
143 - 147 19

1. class limit frequency

9 - 13 1
14 - 19 6
20 - 25 2
26 - 28 5
29 - 32 9

Explanation:

Step1: Calculate class width

The formula for class width \(w=\frac{\text{Range}}{\text{Number of classes}}\). The range \(R = 26 - 7=19\), and the number of classes \(n = 5\). So \(w=\frac{19}{5}=3.8\). Since class width should be a whole number (for simplicity in this context), we round up to \(w = 4\).

Step2: Determine class limits

Start with the minimum value \(7\) as the lower - limit of the first class.

• First class: Lower - limit \(L_1=7\), upper - limit \(U_1 = 7+(4 - 1)=10\) (because if width \(w = 4\), for a class \(a - b\), \(b=a+(w - 1)\)). So the first class is \(7 - 10\).
• Second class: Lower - limit \(L_2=11\), upper - limit \(U_2=11+(4 - 1)=14\), class is \(11 - 14\).
• Third class: Lower - limit \(L_3=15\), upper - limit \(U_3=15+(4 - 1)=18\), class is \(15 - 18\).
• Fourth class: Lower - limit \(L_4=19\), upper - limit \(U_4=19+(4 - 1)=22\), class is \(19 - 22\).
• Fifth class: Lower - limit \(L_5=23\), upper - limit \(U_5=23+(4 - 1)=26\), class is \(23 - 26\).

Answer:

Class width \(w = 4\). Class limits: \(7 - 10\), \(11 - 14\), \(15 - 18\), \(19 - 22\), \(23 - 26\)