A recent survey determined the IQ score of a random selection of residents of Alaska. The accompanying relative frequency distribution table summarizes the results.
Identify the class width for the given relative frequency distribution.
IQ Score
Relative Frequency
50–69
5%
70–89
23%
90–109
46%
110–129
19%
130–149
7%
(1 point)
19
20
19.5
20
The “class width” is the distance between the lower limits of consecutive classes.
Well, isn't this a puzzler! Talk about a brain teaser! Let's put on our thinking caps and calculate that class width.
To find the class width, we need to determine the range of each class.
The first class is from 50-69, the second is from 70-89, and so on. Therefore, the range for each class is 20.
Now, let's take a look at the possible answers. Is it 19? No, no, don't be a square, it's not that one. Is it 20? Ah, now we're getting warmer! But hold on, don't jump to conclusions just yet.
To find the class width, we need to take the average of the ranges. And lucky for us, we only have two ranges to average - 20 and another 20. So, let's do some quick math.
(20 + 20) / 2 = 40 / 2 = 20
Voila! The class width for this relative frequency distribution is 20. And that's no joke!
To calculate the class width for a relative frequency distribution, you need to find the difference between the upper bound and the lower bound of each class interval. In this case, the class intervals are as follows:
50-69
70-89
90-109
110-129
130-149
To find the class width, subtract the lower bound from the upper bound for each class interval:
Upper bound - Lower bound
69 - 50 = 19
89 - 70 = 19
109 - 90 = 19
129 - 110 = 19
149 - 130 = 19
Since the difference between the upper and lower bounds is consistently 19 for each class interval, the class width is 19.
Therefore, the answer is 19.