Understanding Cumulative Frequency from Data

The question provides a frequency distribution table showing different class limits and the number of observations (frequency) falling into each class. We are asked to find the cumulative frequency of the entire data set.

Let's first look at the given data table:

What is Cumulative Frequency?

Cumulative frequency is a running total of frequencies. It tells us how many observations are less than or equal to the upper limit of a particular class. For the first class, the cumulative frequency is the same as its frequency. For subsequent classes, the cumulative frequency is calculated by adding the frequency of the current class to the cumulative frequency of the previous class.

Calculating Cumulative Frequency for Each Class

We can add a cumulative frequency column to the table to see this progression:

Cumulative Frequency of the Entire Data Set

The cumulative frequency of the entire data set is the cumulative frequency of the last class. It represents the total number of observations in the data set. This is also equal to the sum of all frequencies.

Sum of frequencies $\sum f = 4 + 12 + 24 + 40 + 16 + 12 + 10 + 5 + 2$

$\sum f = 125$

As seen from the cumulative frequency column in the table above, the cumulative frequency for the last class (901-1000) is 125.

Final Answer

The cumulative frequency of the entire data set is the total number of observations, which is the sum of all frequencies.

Total Frequency = 125.

Revision Table: Frequency & Cumulative Frequency

Let's quickly recap the key terms:

• Frequency: The number of times a particular value or range of values (class) occurs in a data set.
• Class Limit: The boundaries of a class in a grouped frequency distribution.
• Cumulative Frequency: The sum of the frequencies of a class and all classes below it. It shows the total count up to a certain point in the data.
• Cumulative Frequency of Entire Data Set: The sum of all frequencies in the distribution, representing the total number of observations.

Additional Information: Frequency Distributions and Data Analysis

Frequency distributions like the one provided are fundamental tools in statistics for organizing and summarizing data. They make it easier to understand the pattern of data, such as where most values fall (central tendency) or how spread out the values are (dispersion).

Cumulative frequency distributions are particularly useful for finding percentiles, quartiles, and the median, as they allow us to quickly determine the number or proportion of observations that fall below a certain value.

The total frequency (or the cumulative frequency of the last class) is simply the sample size, which is the total number of data points collected.