The following table gives the life time in days for 100 tubelights. Find the mean life time of tubes by assumed mean method.

To find the mean lifetime of the tubelights using the assumed mean method, we'll follow these steps:

1. Break Down the Problem

1. Prepare a frequency distribution table based on the given lifetime data.
2. Select an assumed mean (A) for calculations.
3. Calculate the deviations from the assumed mean.
4. Calculate the frequency-weighted average of the deviations.
5. Compute the mean using the formula.

2. Relevant Concepts

• The assumed mean method uses the formula: $\text{Mean} = A + \frac{\Sigma f_d}{N}$ where:
  • $A$ = assumed mean
  • $\Sigma f_d$ = sum of the products of frequencies and deviations
  • $N$ = total number of observations (data points)

3. Analysis and Detail

Let's assume that the lifetime distribution data is organized in ranges (not provided, so I'll provide a framework to fill in with data):

1. Choose a suitable assumed mean, $A$. A common practice is to select the midpoint of the data ranges.
2. Calculate the midpoints for each range.
3. Calculate deviations for each midpoint from the assumed mean.
4. Calculate $f \cdot d$ for each range and sum it.

4. Verify and Summarize

Check that the total frequency sums up to 100 and the calculation for the mean is consistent with the values obtained.

Final Answer

• The mean lifetime is calculated as: $\text{Mean} = A + \frac{\Sigma f_d}{N}$
• Substitute the values obtained from the table to find the final mean.

If you provide the actual lifetime data, specific calculations can be conducted for more accurate results.