Question

a professors students keep track of their social interactions for a week. the number of social interactions over the week is shown in the following grouped frequency distribution.
what is the class width?
the class width is
(type a whole number).

Explanation:

Step1: Identify the first class interval

The first class interval is 20 - 28.

Step2: Calculate the class width

To find the class width, we subtract the lower limit from the upper limit of a class interval. For the class 20 - 28, the class width is \( 28 - 20 = 8 \). We can verify with another class, say 29 - 37: \( 37 - 29 = 8 \), and so on. So the class width is consistent across all intervals.

Answer:

9 (Wait, no, let's recalculate. Wait, 28 - 20 is 8? Wait, no, maybe I misread the intervals. Wait the first interval is 20 - 28? Wait, 20 to 28: 28 - 20 = 8? But let's check the next one: 29 - 37. 37 - 29 = 8? Wait 29 to 37 is 8? 37 - 29 = 8. Then 38 - 46: 46 - 38 = 8. 47 - 55: 55 - 47 = 8. 56 - 64: 64 - 56 = 8. 65 - 73: 73 - 65 = 8. 74 - 82: 82 - 74 = 8. 83 - 91: 91 - 83 = 8. 92 - 100: 100 - 92 = 8. 101 - 109: 109 - 101 = 8. Wait, but maybe the first interval is 20 - 28? Wait, 28 - 20 = 8. So the class width is 9? Wait no, 28 - 20 is 8. Wait, maybe I made a mistake. Wait 20 to 28: the difference is 8. But let's check the numbers. Wait 20, 21, ..., 28: that's 9 numbers? Wait no, the class width is the difference between the upper and lower limits, inclusive? No, class width is upper limit - lower limit. So 28 - 20 = 8. But let's check the next interval: 29 - 37. 37 - 29 = 8. So the class width is 9? Wait no, 29 - 20 = 9? Wait, no, the class intervals are consecutive. Wait 20 - 28, then 29 - 37: the difference between 29 and 28 is 1, so the class width is 37 - 29 + 1? No, class width in a frequency distribution is usually calculated as upper limit - lower limit. Wait, maybe the first interval is 20 - 28, so 28 - 20 = 8. But let's check the numbers. Wait 20 to 28: 9 values (20,21,...,28), but class width is 8. Wait, maybe the problem is that the first interval is 20 - 28, so 28 - 20 = 8. But let's see the next interval: 29 - 37. 37 - 29 = 8. So the class width is 9? Wait, no, 29 - 20 = 9? Wait, I think I messed up. Let's take the first two class intervals: 20 - 28 and 29 - 37. The lower limit of the second interval is 29, which is 1 more than the upper limit of the first interval (28). So the class width is 29 - 20 = 9? Wait, no, class width is upper limit of first class - lower limit of first class. So 28 - 20 = 8. But 29 - 28 = 1, so the class width is 8 + 1? No, class width is the difference between the upper and lower bounds of a single class. So for 20 - 28, it's 28 - 20 = 8. But maybe the problem has a typo, or I misread the intervals. Wait, looking at the table: "20-28", "29-37", "38-46", etc. So 28 to 29 is 1, so the class width is 37 - 29 + 1? No, that's the number of values. Class width is 37 - 29 = 8. Wait, but 29 - 20 = 9. Oh! Wait, the class intervals are 20-28, 29-37, 38-46, etc. So the difference between the lower limit of the second class (29) and the lower limit of the first class (20) is 9. So the class width is 9. Ah, that's the mistake. So class width is calculated as the difference between the lower limits of two consecutive classes. So 29 - 20 = 9. Let's check: 38 - 29 = 9, 47 - 38 = 9, 56 - 47 = 9, 65 - 56 = 9, 74 - 65 = 9, 83 - 74 = 9, 92 - 83 = 9, 101 - 92 = 9. Yes! So the class width is 9. Because the lower limit of the next class is 9 more than the lower limit of the previous class. So 20, 29, 38, ...: each time +9. So the class width is 9.

Step1: Find the lower limit of the first class

The first class is 20 - 28, so the lower limit is 20.

Step2: Find the lower limit of the second class

The second class is 29 - 37, so the lower limit is 29.

Step3: Calculate the class width

Subtract the lower limit of the first class from the lower limit of the second class: \( 29 - 20 = 9 \).