Data handling refers to the process of collecting, organising, and interpreting numerical information. In daily life, data helps us make decisions — from weather forecasts to school results.
Collecting and Organising Data:
Raw data is unorganised information. We organise it using tally marks and frequency tables. A frequency table shows how many times each value (or group of values) appears.
Arithmetic Mean (Average):
Mean = Sum of all observations / Number of observations
The mean is a measure of the central tendency of a data set — it represents a typical value.
- Median:
- The median is the middle value when data is arranged in order.
- If there is an odd number of values, the median is the middle one.
- If there is an even number of values, the median is the average of the two middle values.
Mode:
The mode is the value that appears most frequently in a data set. A data set may have one mode, more than one mode, or no mode.
Range:
Range = Maximum value - Minimum value. It tells us how spread out the data is.
Bar Graphs:
A bar graph uses rectangular bars of equal width to represent data. The height (or length) of the bar indicates the frequency or value.
Chance and Probability:
Probability is a measure of how likely an event is.
P(event) = Number of favourable outcomes / Total number of outcomes
Probability is always between 0 (impossible) and 1 (certain).
The marks of 7 students are: 45, 60, 55, 70, 60, 50, 60. Find the mean.
Mean = (45+60+55+70+60+50+60)/7 = 400/7 = approximately 57.1.
Find the median of 4, 7, 2, 9, 5, 1, 6.
Arranged in order: 1, 2, 4, 5, 6, 7, 9. There are 7 values. Middle value = 4th value = 5. Median = 5.
Find the mode of 3, 5, 3, 7, 5, 3, 8.
3 appears 3 times, 5 appears 2 times, others appear once. Mode = 3.
Find the range of 12, 7, 19, 4, 15.
Range = 19 - 4 = 15.
A bag contains 3 red, 5 blue, 2 green balls. What is the probability of picking a blue ball?
P(blue) = 5 / (3+5+2) = 5/10 = 1/2.
The mean of five numbers is 12. If four of them are 10, 14, 9, 13, find the fifth.
Sum = 5 x 12 = 60. Sum of four = 10+14+9+13 = 46. Fifth number = 60 - 46 = 14.
A coin is tossed once. What is the probability of getting tails?
Total outcomes = 2 (heads or tails). Favourable = 1. P(tails) = 1/2.
- Key Formulas:
- Mean = Sum of observations / Number of observations
- P(event) = Favourable outcomes / Total outcomes
- Range = Maximum - Minimum
Common mistakes
Do not forget to arrange data in order before finding the median. For probability, make sure to include ALL possible outcomes in the denominator, not just the favourable ones.
Summary
Data handling involves organising data and computing measures like mean, median, mode, and range. Probability gives us a way to predict outcomes. These tools help interpret real-world information effectively.