Question

the data represent the time, in minutes, spent reading a political blog in a day. construct a frequency distribution using 5 classes. in the table, include the midpoints, relative frequencies, and cumulative frequencies. which class has the greatest frequency and which has the least frequency?
17 2 8 5 6
7 21 14 8 9
7 3 8 1 10
28 27 1 0 29
complete the table, starting with the lowest class limit.
(simplify your answers.)
class frequency midpoint relative frequency cumulative frequency
which class has the greatest frequency?
the class with the greatest frequency is from □ to □
which class has the least frequency?
the class with the least frequency is from □ to □

Explanation:

Step1: Find Range

First, find the minimum and maximum values. From the data: min = 0, max = 29. Range = \( 29 - 0 = 29 \).

Step2: Determine Class Width

Number of classes = 5. Class width = \( \lceil \frac{29}{5}
ceil = 6 \) (ceiling of 5.8 is 6).

Step3: Define Classes

Classes: 0 - 5, 6 - 11, 12 - 17, 18 - 23, 24 - 29.

Step4: Count Frequencies

Count data in each class:

• 0 - 5: 0,1,2,3,5 → 5
• 6 - 11: 6,7,7,8,8,8,9,10 → 8
• 12 - 17: 14,17 → 2? Wait, wait, recheck data: 17,2,8,5,6,7,21,14,8,9,7,3,8,1,10,28,27,1,0,29. Wait, full data: let's list all: 0,1,2,3,5,6,7,7,8,8,8,9,10,14,17,21,27,28,29,1 (wait, maybe I missed. Let's count total: 20 data points? Wait, the data: 17,2,8,5,6,7,21,14,8,9,7,3,8,1,10,28,27,1,0,29. Yes, 20 points.

Now classes:
0 - 5: 0,1,2,3,5,1,1 → Wait, 0,1,2,3,5,1,1? Wait no, 0,1,2,3,5,1,1? Wait, data points: 0,1,2,3,5,1,1? No, let's list each:
0,1,2,3,5,6,7,7,8,8,8,9,10,14,17,21,27,28,29,1. Wait, 20 points. Let's sort: 0,1,1,2,3,5,6,7,7,8,8,8,9,10,14,17,21,27,28,29.
Now classes:
0 - 5: 0,1,1,2,3,5 → 6 (wait, 0,1,1,2,3,5: 6 points)
6 - 11: 6,7,7,8,8,8,9,10 → 8 points
12 - 17: 14,17 → 2 points
18 - 23: 21 → 1 point
24 - 29: 27,28,29 → 3 points
Wait, that sums to 6+8+2+1+3=20. Correct.

Step5: Identify Max and Min Frequencies

Frequency for 0-5:6, 6-11:8, 12-17:2, 18-23:1, 24-29:3.
Greatest frequency: 6-11 (8). Least frequency: 18-23 (1).

Answer:

The class with the greatest frequency is from 6 to 11.
The class with the least frequency is from 18 to 23.