Frequency Distributions

Step 1: Recall definitions of statistical terms.

• Class interval: The range of values in a class in grouped data.
• Frequency: The number of times a particular observation occurs.
• Cumulative frequency: The running total of frequencies up to a certain point.
• Range: The difference between the maximum and minimum observations in a data set.

Step 2: Match the definition to the problem.

The difference between the maximum and minimum observations is called the range.

Final Answer: The correct term is , which corresponds to option .

Given: The mean of the frequency distribution is 15.

Step 1: Understanding the Mean Formula

The mean is given by:

Where:

• = Frequency
• = Midpoint of class
• = Product of and
• = Sum of all values
• = Sum of all frequencies

Step 2: Calculating and

Calculating for given values:

Calculating :

Step 3: Substituting into Mean Formula

Multiplying both sides by :

Rearranging:

Final Answer:

Step 1: Identify the Class Intervals and Frequencies

Given a cumulative frequency distribution, we determine the class intervals:

Step 2: Identify the Modal Class

The modal class is the class with the highest frequency. From the table above, the highest frequency is 30, which corresponds to the class interval 30 - 40.

Final Answer: 30 - 40