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The table in the image represents the lifetime of electricity tubes in days and their corresponding frequency (number of tubes). The data is grouped as follows:

- Less than 50 days: 8 tubes
- Less than 100 days: 23 tubes
- Less than 150 days: 55 tubes
- Less than 200 days: 81 tubes
- Less than 250 days: 93 tubes
- Less than 300 days: 100 tubes

Since the intervals are cumulative, the number of tubes in each specific range can be determined by subtraction. For example, the number of tubes in the range 50-100 days can be calculated as:
\[
23 - 8 = 15 \text{ tubes}
\]
We can follow this approach to find the number of tubes for each range and proceed to calculate the mean lifetime.

Let me perform these steps and calculate the mean lifetime of the tubes.The number of tubes in each specific lifetime range is as follows:

- 0 to 50 days: 8 tubes
- 50 to 100 days: 15 tubes
- 100 to 150 days: 32 tubes
- 150 to 200 days: 26 tubes
- 200 to 250 days: 12 tubes
- 250 to 300 days: 7 tubes

The mean lifetime of the electricity tubes is **145 days**.

Would you like more details or have any questions?

Here are five related questions you might find helpful:
1. How do we calculate the weighted mean for grouped data?
2. What is the significance of the midpoint in such a frequency distribution?
3. How would you calculate the median from this data?
4. What would the variance and standard deviation be for this dataset?
5. How could this data be represented graphically?

**Tip:** When calculating the mean from grouped data, always use the midpoints of the intervals as representative values for the data within each group.

Estimate the mean lifetime of electricity tubes based on the cumulative frequency distribution table provided.

Learn how to estimate the mean lifetime of electricity tubes based on a cumulative frequency distribution table. The problem involves calculating the mean using the formula for grouped data, suitable for students in Grades 9-11.

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