Question

class width, class midpoints, and class boundaries.
table with columns: frequency, midpoint, class boundaries; rows: frequency 1 (midpoint 37, class boundaries with \type your answer...\), frequency 3 (midpoint 42, class boundaries with \type your answer...\), frequency 5 (midpoint 47, class boundaries with \type your answer...\), frequency 11 (midpoint 52, class boundaries with \type your answer...\), frequency 7 (midpoint 57, class boundaries with \type your answer...\), frequency 7 (midpoint 62, class boundaries with \type your answer...\)

Explanation:

Step1: Find class width

The midpoints are 37, 42, 47, 52, 57, 62. The difference between consecutive midpoints is \(42 - 37 = 5\), so class width \(w = 5\).

Step2: Find class boundaries for first class (midpoint 37)

Lower boundary: \(37 - \frac{5}{2}=37 - 2.5 = 34.5\)
Upper boundary: \(37 + \frac{5}{2}=37 + 2.5 = 39.5\)

Step3: Find class boundaries for second class (midpoint 42)

Lower boundary: \(42 - \frac{5}{2}=42 - 2.5 = 39.5\) (same as upper boundary of previous class)
Upper boundary: \(42 + \frac{5}{2}=42 + 2.5 = 44.5\)

Step4: Find class boundaries for third class (midpoint 47)

Lower boundary: \(47 - \frac{5}{2}=47 - 2.5 = 44.5\)
Upper boundary: \(47 + \frac{5}{2}=47 + 2.5 = 49.5\)

Step5: Find class boundaries for fourth class (midpoint 52)

Lower boundary: \(52 - \frac{5}{2}=52 - 2.5 = 49.5\)
Upper boundary: \(52 + \frac{5}{2}=52 + 2.5 = 54.5\)

Step6: Find class boundaries for fifth class (midpoint 57)

Lower boundary: \(57 - \frac{5}{2}=57 - 2.5 = 54.5\)
Upper boundary: \(57 + \frac{5}{2}=57 + 2.5 = 59.5\)

Step7: Find class boundaries for sixth class (midpoint 62)

Lower boundary: \(62 - \frac{5}{2}=62 - 2.5 = 59.5\)
Upper boundary: \(62 + \frac{5}{2}=62 + 2.5 = 64.5\)

Answer:

Frequency	Midpoint	Class Boundaries
3	42	39.5 - 44.5
5	47	44.5 - 49.5
11	52	49.5 - 54.5
7	57	54.5 - 59.5
7	62	59.5 - 64.5