A frequency distribution of the life times of 400 T.V. picture tubes tested in a tube company is given below. Find the average life of tube. Life Time (in hrs)                          Frequency                          Life time (in hrs)                          Frequency 300-399 400-499 500-599 600-699 700-799     14 46 58 76 68  800-899 900-999 1000-1099 1100-1199 62 48 22 6

Explanation

To find the average life of the TV picture tubes based on the given frequency distribution, we will follow these steps:

### Step 1: Create a Table of Mid-values
We need to calculate the mid-values for each class interval. The mid-value (xi) for a class interval can be calculated as:
\[ \text{Mid-value} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \]

| Life Time (in hrs) | Frequency (fi) | Mid-value (xi) |
|---------------------|----------------|-----------------|
...