Data Handling Word Problems
What is Data Handling Word Problems - Grade 7 Maths (Data Handling)?
Key formulas:
- Mean = Sum of all values ÷ Number of values
- Median = Middle value when data is arranged in order
- Mode = Value that appears most often
- Range = Highest value − Lowest value
Data Handling Word Problems Formula
Finding missing value from mean:
Sum of values = Mean × Number of values
If one value is unknown, find the total using the mean, subtract the known values, and the remainder is the missing value.
Types and Properties
Common problem types:
- Find mean/median/mode from given data.
- Find a missing value when the mean is given.
- Find how adding/removing a value changes the mean.
- Compare two data sets using their averages.
Solved Examples
Example 1: Finding the Mean
Problem: Marks of 5 students: 72, 85, 90, 68, 80. Find the mean.
Solution:
- Sum = 72 + 85 + 90 + 68 + 80 = 395
- Mean = 395 ÷ 5 = 79
Answer: Mean = 79.
Example 2: Finding Missing Value
Problem: The mean of 4 numbers is 25. Three of them are 20, 30, 22. Find the fourth.
Solution:
- Total = 25 × 4 = 100
- Fourth number = 100 − (20 + 30 + 22) = 100 − 72 = 28
Answer: 28.
Example 3: Finding Median
Problem: Data: 15, 8, 22, 17, 11. Find the median.
Solution:
- Arrange in order: 8, 11, 15, 17, 22
- Middle value (3rd out of 5) = 15
Answer: Median = 15.
Example 4: Effect of Adding a Value
Problem: Mean of 5 numbers is 40. A sixth number (70) is added. Find the new mean.
Solution:
- Old total = 40 × 5 = 200
- New total = 200 + 70 = 270
- New mean = 270 ÷ 6 = 45
Answer: New mean = 45.
Real-World Applications
Real-world uses:
- Exams: Finding average marks, identifying top scores.
- Weather: Average temperature over a week.
- Sports: Batting average, average goals per match.
- Business: Average sales per day, most popular product (mode).
Key Points to Remember
- Mean = Sum ÷ Count.
- To find a missing value: missing = (Mean × Count) − Sum of known values.
- Median requires data to be arranged in order first.
- Mode is the most frequent value (there can be more than one mode).
- Adding a value above the mean increases the mean; below the mean decreases it.
Practice Problems
- Find the mean of: 14, 22, 18, 26, 20.
- The mean of 6 numbers is 15. Five of them are 10, 12, 18, 20, 14. Find the sixth.
- Find the median of: 3, 7, 1, 9, 5, 2, 8.
- Runs scored in 5 innings: 45, 67, 45, 80, 45. Find the mode.
Frequently Asked Questions
Q1. How do you find a missing value when the mean is given?
Multiply the mean by the number of values to get the total. Subtract the sum of known values. The result is the missing value.
Q2. What if there are two middle values for the median?
If the number of values is even, the median is the average of the two middle values. For example, for 2, 4, 6, 8: median = (4 + 6)/2 = 5.
Q3. Can there be no mode?
Yes. If all values appear equally often, there is no mode. For example, 3, 5, 7, 9 has no mode.
