the class mark of the observation are 17, 21, 25, 29, 33,37,41,45.find the class intervals
To find the class intervals, we need to determine the range and the number of class intervals.
1. Range: The range is the difference between the largest and smallest values in the data set. In this case, the smallest value is 17, and the largest value is 45. So the range is 45 - 17 = 28.
2. Number of Class Intervals: The number of class intervals helps organize the data into meaningful groups. There is no fixed rule for determining the number of intervals, but a common guideline is to use between 5 to 20 intervals. In this case, let's choose 5 class intervals for simplicity.
To calculate the interval length, we divide the range by the number of class intervals:
Interval Length = Range / Number of Intervals = 28 / 5 = 5.6
Now, to find the class intervals, we start by determining the lower limit of the first interval:
First Lower Limit = Smallest Value - (Interval Length / 2) = 17 - (5.6 / 2) = 17 - 2.8 = 14.2 (rounded to one decimal place)
We can use this value as the lower limit of the first interval. To find the upper limit, we add the interval length to the lower limit:
First Upper Limit = First Lower Limit + Interval Length = 14.2 + 5.6 = 19.8 (rounded to one decimal place)
Therefore, the first class interval is 14.2 - 19.8.
Now we continue to find the subsequent class intervals:
Second Lower Limit = First Upper Limit + 0.1 = 19.8 + 0.1 = 19.9
Second Upper Limit = Second Lower Limit + Interval Length = 19.9 + 5.6 = 25.5
Third Lower Limit = Second Upper Limit + 0.1 = 25.5 + 0.1 = 25.6
Third Upper Limit = Third Lower Limit + Interval Length = 25.6 + 5.6 = 31.2
Fourth Lower Limit = Third Upper Limit + 0.1 = 31.2 + 0.1 = 31.3
Fourth Upper Limit = Fourth Lower Limit + Interval Length = 31.3 + 5.6 = 36.9
Fifth Lower Limit = Fourth Upper Limit + 0.1 = 36.9 + 0.1 = 37
Fifth Upper Limit = Fifth Lower Limit + Interval Length = 37 + 5.6 = 42.6
The class intervals are as follows:
1. 14.2 - 19.8
2. 19.9 - 25.5
3. 25.6 - 31.2
4. 31.3 - 36.9
5. 37 - 42.6