The question asks to find the mean using the assumed mean method and to verify the result using the direct method. Here's a breakdown of how to approach this:

Given Data:

The table provided has two columns:

1. Assumed Mean Method:

In this method, we take an assumed mean $A$, calculate deviations $d_i = x_i - A$, and then apply the formula: $\bar{x} = A + \frac{\sum{f_i d_i}}{\sum{f_i}}$ where:

• $\bar{x}$ is the mean,
• $f_i$ is the frequency of the $i$-th variable,
• $d_i = x_i - A$, and
• $A$ is the assumed mean.

From the question, we are told to assume $A = 16$ (you can pick a different value, but 16 is near the middle).

Steps:

1. Calculate $d_i = x_i - 16$ for each $x$ value.
2. Multiply $f_i$ by $d_i$.
3. Apply the formula for the mean.

2. Direct Method:

In the direct method, we use the formula: $\bar{x} = \frac{\sum{f_i x_i}}{\sum{f_i}}$ Here, we multiply each frequency by its corresponding variable, sum the products, and then divide by the total frequency.

I can calculate both methods for you if you'd like. Would you prefer a detailed step-by-step solution, or should I directly compute the final answer for both methods?