The government rescued 100 people after a train accident. Their ages were recorded in the following table. Find their mean age.
| Age (in years) | Number of people rescued |
|---|---|
| 10 - 20 | 9 |
| 20 - 30 | 14 |
| 30 - 40 | 15 |
| 40 - 50 | 21 |
| 50 - 60 | 23 |
| 60 - 70 | 12 |
| 70 - 80 | 6 |
Get the complete, step-by-step math solution for: "The government rescued 100 people after a train accident. Their ages were recorded in the following table. Find their mean age. | Age (in years) | Num...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Calculate Class Marks
To find the mean of grouped data, we first need to determine the class mark (xi) for each age group. The class mark is the midpoint of each class interval, calculated by adding the lower and upper limits of the class and dividing by 2.
Step 2: Calculate fixi
Next, we multiply the frequency (fi) of each class by its corresponding class mark (xi). This gives us the product fixi for each age group, which represents the sum of ages for that group.
Step 3: Calculate Sum of fixi and Sum of fi
Now, we sum all the fixi values to get the total sum of ages for all rescued people. We also sum all the frequencies (fi) to get the total number of people, which is given as 100.
Step 4: Calculate Mean Age
Finally, we calculate the mean age by dividing the sum of fixi by the sum of fi. This formula gives us the average age of the rescued people.
Step 5: Substitute Values and Solve
Substituting the calculated values into the mean formula, we find that the mean age of the rescued people is 44 years.