alright this is gonna take me a while to type out:
To construct a frequency distribution with 5 classes, we first need to find the range of the data:
Maximum value: 29
Minimum value: 0
Range = Maximum value - Minimum value = 29 - 0 = 29
Next, we determine the width of each class:
\[ \text{Width of each class} = \frac{\text{Range}}{\text{Number of classes}} = \frac{29}{5} = 5.8 \]
Since it's not practical to have a decimal value for the width of a class, we round it up to the nearest whole number, which is 6.
Now, we can construct the classes:
Class 1: 0 - 5
Class 2: 6 - 11
Class 3: 12 - 17
Class 4: 18 - 23
Class 5: 24 - 29
Next, we count the frequencies of the data points falling into each class:
Class 1 (0 - 5): 2
Class 2 (6 - 11): 3
Class 3 (12 - 17): 2
Class 4 (18 - 23): 5
Class 5 (24 - 29): 5
To find the midpoint of each class, we take the average of the lower and upper limits:
Class 1 (0 - 5): Midpoint = (0 + 5) / 2 = 2.5
Class 2 (6 - 11): Midpoint = (6 + 11) / 2 = 8.5
Class 3 (12 - 17): Midpoint = (12 + 17) / 2 = 14.5
Class 4 (18 - 23): Midpoint = (18 + 23) / 2 = 20.5
Class 5 (24 - 29): Midpoint = (24 + 29) / 2 = 26.5
Now, we calculate the relative frequency for each class by dividing the frequency of each class by the total number of data points (which is 19 in this case):
Relative Frequency = Frequency / Total number of data points = Frequency / 19
Finally, we calculate the cumulative frequency by adding up the frequencies as we move down the table.
Ive shown the table in the image i added
