Answer:
a) See attachment 1.
b) See attachment 2.
c) 34 years
Step-by-step explanation:
Part (a)
Cumulative frequency refers to the running total of frequencies.
For the class interval 0 < a ≤ 20, the cumulative frequency is the same as the frequency of the class interval 0 < a ≤ 20, which is 7.
For the class interval 0 < a ≤ 30, the cumulative frequency is the sum of the frequency of the class intervals 0 < a ≤ 20 and 20 < a ≤ 30, which is 7 + 25 = 32.
For the class interval 0 < a ≤ 40, the cumulative frequency is the sum of the frequency of the class intervals 0 < a ≤ 30 and 30 < a ≤ 40, which is 32 + 20 = 52.
Continue this process for each subsequent row:
0 < a ≤ 20: 7
0 < a ≤ 30: 7 + 25 = 32
0 < a ≤ 40: 32 + 20 = 52
0 < a ≤ 50: 52 + 14 = 66
0 < a ≤ 60: 66 + 8 = 74
0 < a ≤ 70: 74 + 6 = 80
See attachment 1.
[tex]\dotfill[/tex]
Part (b)
To draw a cumulative frequency graph from the cumulative frequency table:
- Plot the upper class limits on the x-axis and the corresponding cumulative frequencies on the y-axis.
- Connect the points plotted on the graph with straight lines, joining each point to the previous one.
- Extend the first line to the y-axis at y = 0.
So the points to plot are:
- (0, 0)
- (20, 7)
- (30, 32)
- (40, 52)
- (50, 66)
- (60, 74)
- (70, 80)
See attachment 2.
[tex]\dotfill[/tex]
Part (c)
To use the graph to find an estimate for the median age of the 80 people, first calculate the median position which is half of the total frequency:
[tex]\textsf{Median position}=\dfrac{80}{2}=40[/tex]
Now, draw a horizontal line from this point until it intersects the cumulative frequency polygon. The corresponding value on the x-axis gives you an estimate for the median age.
Therefore, the median age is 34 years.
See attachment 3.
