Question: Find the mean and the mode for the following frequency distribution. \[ \begin{array}{c|c} x & f…

Find the mean and the mode for the following frequency distribution.

\[ \begin{array}{c|c} x & f \\ \hline 2 & 4 \\ 3 & 4 \\ 4 & 3 \\ 5 & 2 \\ 6 & 0 \\ \end{array} \]

Solution

To find the mean and mode for the given frequency distribution, follow these steps: Mean Calculation: 1. Calculate the sum of the products of each value and its frequency. \[ \text{Sum of } xf = 2 \times 4 + 3 \times 4 + 4 \times 3 + 5 \times 2 + 6 \times 0 \] \[ = 8 + 12 + 12 + 10 + 0 \] \[ = 42 \] 2. Calculate the total frequency. \[ \text{Total frequency } = 4 + 4 + 3 + 2 + 0 = 13 \] 3. Calculate the mean. \[ \text{Mean} = \frac{\text{Sum of } xf}{\text{Total frequency}} = \frac{42}{13} \approx 3.23 \] Mode: The mode is the value with the highest frequency. From the frequency distribution, the value 2 and 3 both have the highest frequency of 4. Thus, the mode is 2 and 3 (bimodal distribution).