Questions: Find the frequencies. Class limits Class boundaries Frequency 15-19 14.5-19.5 20-24 19.5-24.5 25-29 24.5-29.5 30-34 29.5-34.5 35-39 34.5-39.5 Total Frequency =

Solution Steps

To find the frequencies for each class, you need to count the number of data points that fall within each class boundary. This involves iterating over the dataset and checking which class boundary each data point falls into. Once you have counted the data points for each class, you can sum these frequencies to get the total frequency.

The class boundaries are defined as follows:

• Class 1: \(14.5 < x \leq 19.5\)
• Class 2: \(19.5 < x \leq 24.5\)
• Class 3: \(24.5 < x \leq 29.5\)
• Class 4: \(29.5 < x \leq 34.5\)
• Class 5: \(34.5 < x \leq 39.5\)

For each class, count the number of data points that fall within the class boundaries:

• Class 1: Data points \(16, 18\) fall within \(14.5 < x \leq 19.5\). Frequency = 2.
• Class 2: Data points \(22, 23\) fall within \(19.5 < x \leq 24.5\). Frequency = 2.
• Class 3: Data points \(27, 28\) fall within \(24.5 < x \leq 29.5\). Frequency = 2.
• Class 4: Data points \(31, 33\) fall within \(29.5 < x \leq 34.5\). Frequency = 2.
• Class 5: Data points \(36, 37\) fall within \(34.5 < x \leq 39.5\). Frequency = 2.

Sum the frequencies of all classes to find the total frequency: \[ \text{Total Frequency} = 2 + 2 + 2 + 2 + 2 = 10 \]

Final Answer