For calculating the mean of grouped data, the direct method is usually the simplest and fastest, especially when the numbers (frequencies and class marks) are small. Always double-check your arithmetic, as a small calculation error can lead to a wrong answer.
Step 1: Understanding the Concept:
To find the mean of grouped data, we use the direct method, which involves finding the class mark (mid-point) for each class interval, multiplying it by the corresponding frequency, summing these products, and then dividing by the total frequency. Step 2: Key Formula or Approach:
The formula for the mean (\(\bar{x}\)) of grouped data is:
\[ \bar{x} = \frac{\sum f_i x_i}{\sum f_i} \]
where \(f_i\) is the frequency of the \(i\)-th class and \(x_i\) is the class mark of the \(i\)-th class.
The class mark \(x_i\) is calculated as \( \frac{\text{Upper limit} + \text{Lower limit}}{2} \). Step 3: Detailed Explanation:
We will create a table to organize the calculations.
First, calculate the total frequency (\(\sum f_i\)):
\[ \sum f_i = 4 + 2 + 1 + 3 = 10 \]
Next, calculate the sum of the products of frequency and class mark (\(\sum f_i x_i\)):
\[ \sum f_i x_i = 16 + 12 + 8 + 30 = 66 \]
Now, use the formula for the mean:
\[ \bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{66}{10} = 6.6 \]
Step 4: Final Answer:
The mean from the given table is 6.6.
