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 |

Step 1: Calculate Class Marks

To find the mean of grouped data, we first need to determine the class mark ($x_i$) 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 $f_i x_i$

Next, we multiply the frequency ($f_i$) of each class by its corresponding class mark ($x_i$). This gives us the product $f_i x_i$ for each age group, which represents the sum of ages for that group.

Step 3: Calculate Sum of $f_i x_i$ and Sum of $f_i$

Now, we sum all the $f_i x_i$ values to get the total sum of ages for all rescued people. We also sum all the frequencies ($f_i$) 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 $f_i x_i$ by the sum of $f_i$. 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.

More from this chapter

• **Example 6.** Find mean of the following data. | Class | 0-15 | 15-30 | 30-45 | 45-60 | 60-75 | 75-90 | |:---: |:---: |:---: |:---: |:---: |:---: |:---: | | **
• Example 2. The mean of the following data is 14. Find the value of k. |c|c|c|c|c|c| x & 5 & 10 & 15 & 20 & 25 f & 7 & k & 8 & 4 & 5
• Find the mean of the following frequency distribution: class intervals 0-10, 10-20, 20-30, 30-40, 40-50 with frequencies 5, 8, 15, 16, 6.
• Find the mean of 4, 8, 15, 16, 23, 42
• The marks obtained by 50 students in a test are tabulated below: | Marks: | 0 - 15 | 15 - 30 | 30 - 45 | 45 - 60 | 60 - 75 | |---|---|---|---|---|---| | Number
• A survey regarding the heights (in cm) of 50 girls of class X of a school was conducted and the following data was obtained: | Height (in cm) | Number of girls
• In the following table, the median age of 200 spectators of a football match is 32. Find the missing frequencies p and q. | Age (in years) | Number of Spectator
• Using empirical relationship, the mode of a distribution whose mean is 7.2 and the median 7.1, is:

All Statistics solutions →