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Answer:
The number of individuals included in the summary is 146.
Step-by-step explanation:
The frequency distribution table provided is as follows:
Class Intervals Frequency
100 - 199 24
200 - 299 90
300 - 399 27
400 - 499 1
500 - 599 4
The lower class limit it the smallest value of each class interval.
Lower class limit = {100, 200, 300, 400, 500}
The upper class limit it the highest value of each class interval.
Upper class limit = {199, 299, 399, 499, 599}
The lower class boundaries are the lower class limits decreased by 0.5 and the upper class boundaries are the upper class limits increased by 0.5.
Class boundaries:
99.5 - 199.5
199.5 - 299.5
299.5 - 399.5
399.5 - 499.5
499.5 - 599.5
The class width is the difference between the class boundaries of each class.
Class width = 199.5 - 99.5 = 100
So, the class width is 100.
The midpoints of a class is the average value of the boundaries of a class.
[tex]\text{Midpoint}_{100-199}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\[/tex]
[tex]=\frac{99.5+199.5}{2}\\\\=149.5[/tex]
[tex]\text{Midpoint}_{200-299}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\[/tex]
[tex]=\frac{199.5+299.5}{2}\\\\=249.5[/tex]
[tex]\text{Midpoint}_{300-399}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\[/tex]
[tex]=\frac{299.5+399.5}{2}\\\\=349.5[/tex]
[tex]\text{Midpoint}_{400-499}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\[/tex]
[tex]=\frac{399.5+499.5}{2}\\\\=449.5[/tex]
[tex]\text{Midpoint}_{500-599}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\[/tex]
[tex]=\frac{499.5+599.5}{2}\\\\=549.5[/tex]
The number of individuals included in the summary is the sum of all frequencies.
[tex]\text{Number of Individuals}=24 + 90 + 27 + 1 + 4=146[/tex]
Thus, the number of individuals included in the summary is 146.
Lower class limits are the smallest numbers of the class intervals in continuous series. Lower class limits are = 100 , 200 , 300 , 400 , 500
Upper class limits are the largest numbers of the class intervals in continuous series. Upper Class limits are = 199 , 299 , 399 , 499 , 599
Class Boundaries are Inclusive Continuous series converted into Exclusive Continuous series. It is done with half the difference of upper class limit & lower class limit of preceding and successive class interval respectively, like 1/2 (200 - 199) = 0.5 & so on.
This difference is then subtracted from lower limit and added to upper limit of each class interval, like 100 - 0.5 = 99.5 & 199 + 0.5 = 199.5 & so on.
Class Width is the difference between Upper and Lower class boundaries of Exclusive Series Class Width, it is equal to 199.5 - 99.5 = 99 & so on.
Number of Individuals included in summary is the summation of frequency, = 24 + 90 + 27 + 1 + 4 = 146
Class midpoint is average of upper and lower class boundaries, = (upper class + lower class boundary) / 2
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