The midpoints or class marks for the ages of the factory workers are 19.5, 29.5, 39.5, 49.5, 59.5 and 69.5. What are the class limits of this distribution??
Find the average of two adjacent midpoints; for example:
(29.5 + 39.5)/2 = 34.5
34.5 is the class boundary between the two classes whose midpoints are 29.5 and 39.5.
Drop and raise that value a half-point for the class limits:
34.5 - .5 = 34
34.5 + .5 = 35
Thus we have , so far:
Midpoint.....Class Limits
29.5........... ___ - 34
39.5 .......... 35 - ___
Work with more adjacent pairs of midpoints to fill in the rest of the class limits.
To find the class limits of this distribution, we need to determine the lower and upper limits for each class interval.
Since the midpoints are given, we can assume that each class interval has the same width.
Let's assume the width of each interval is denoted by 'w'.
To find the lower limit of the first class, we can subtract half of the width from the midpoint:
Lower limit of the first class = 19.5 - (w/2)
Similarly, the upper limit of the first class can be found by adding half of the width to the midpoint:
Upper limit of the first class = 19.5 + (w/2)
Since the midpoints for the ages are given as 19.5, 29.5, 39.5, 49.5, 59.5, and 69.5, we can follow the same steps to determine the lower and upper limits for each class:
1st class lower limit = 19.5 - (w/2)
1st class upper limit = 19.5 + (w/2)
2nd class lower limit = 29.5 - (w/2)
2nd class upper limit = 29.5 + (w/2)
3rd class lower limit = 39.5 - (w/2)
3rd class upper limit = 39.5 + (w/2)
4th class lower limit = 49.5 - (w/2)
4th class upper limit = 49.5 + (w/2)
5th class lower limit = 59.5 - (w/2)
5th class upper limit = 59.5 + (w/2)
6th class lower limit = 69.5 - (w/2)
6th class upper limit = 69.5 + (w/2)
Please note that the value of 'w' is required to accurately determine the class limits for each interval.
To determine the class limits, we need to understand what the midpoints or class marks represent. The class marks are the middle values of each class interval, calculated by taking the average of the upper and lower limits of each class interval.
In this case, since the given class marks are 19.5, 29.5, 39.5, 49.5, 59.5, and 69.5, we can assume that each class interval has a width of 10 and is symmetrically distributed around the midpoints.
To find the class limits, we can subtract and add half of the class width to each class mark.
For the first class mark, 19.5, subtracting 5 from 19.5 gives the lower class limit of 14.5, and adding 5 to 19.5 gives the upper class limit of 24.5.
Similarly, for the other class marks:
- For 29.5, the lower class limit is 24.5 and the upper class limit is 34.5.
- For 39.5, the lower class limit is 34.5 and the upper class limit is 44.5.
- For 49.5, the lower class limit is 44.5 and the upper class limit is 54.5.
- For 59.5, the lower class limit is 54.5 and the upper class limit is 64.5.
- For 69.5, the lower class limit is 64.5 and the upper class limit is 74.5.
Therefore, the class limits for this distribution are:
- 14.5 - 24.5
- 24.5 - 34.5
- 34.5 - 44.5
- 44.5 - 54.5
- 54.5 - 64.5
- 64.5 - 74.5