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.
![\text{Midpoint}_{100-199}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\](https://tex.z-dn.net/?f=%5Ctext%7BMidpoint%7D_%7B100-199%7D%3D%5Cfrac%7B%5Ctext%7BLower%20class%20boundary%7D%20%2B%20%5Ctext%7BUpper%20class%20boundary%7D%7D%7B2%7D%5C%5C)
![=\frac{99.5+199.5}{2}\\\\=149.5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B99.5%2B199.5%7D%7B2%7D%5C%5C%5C%5C%3D149.5)
![\text{Midpoint}_{200-299}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\](https://tex.z-dn.net/?f=%5Ctext%7BMidpoint%7D_%7B200-299%7D%3D%5Cfrac%7B%5Ctext%7BLower%20class%20boundary%7D%20%2B%20%5Ctext%7BUpper%20class%20boundary%7D%7D%7B2%7D%5C%5C)
![=\frac{199.5+299.5}{2}\\\\=249.5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B199.5%2B299.5%7D%7B2%7D%5C%5C%5C%5C%3D249.5)
![\text{Midpoint}_{300-399}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\](https://tex.z-dn.net/?f=%5Ctext%7BMidpoint%7D_%7B300-399%7D%3D%5Cfrac%7B%5Ctext%7BLower%20class%20boundary%7D%20%2B%20%5Ctext%7BUpper%20class%20boundary%7D%7D%7B2%7D%5C%5C)
![=\frac{299.5+399.5}{2}\\\\=349.5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B299.5%2B399.5%7D%7B2%7D%5C%5C%5C%5C%3D349.5)
![\text{Midpoint}_{400-499}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\](https://tex.z-dn.net/?f=%5Ctext%7BMidpoint%7D_%7B400-499%7D%3D%5Cfrac%7B%5Ctext%7BLower%20class%20boundary%7D%20%2B%20%5Ctext%7BUpper%20class%20boundary%7D%7D%7B2%7D%5C%5C)
![=\frac{399.5+499.5}{2}\\\\=449.5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B399.5%2B499.5%7D%7B2%7D%5C%5C%5C%5C%3D449.5)
![\text{Midpoint}_{500-599}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\](https://tex.z-dn.net/?f=%5Ctext%7BMidpoint%7D_%7B500-599%7D%3D%5Cfrac%7B%5Ctext%7BLower%20class%20boundary%7D%20%2B%20%5Ctext%7BUpper%20class%20boundary%7D%7D%7B2%7D%5C%5C)
![=\frac{499.5+599.5}{2}\\\\=549.5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B499.5%2B599.5%7D%7B2%7D%5C%5C%5C%5C%3D549.5)
The number of individuals included in the summary is the sum of all frequencies.
![\text{Number of Individuals}=24 + 90 + 27 + 1 + 4=146](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20Individuals%7D%3D24%20%2B%2090%20%2B%2027%20%2B%201%20%2B%204%3D146)
Thus, the number of individuals included in the summary is 146.