Data is a collection of facts, numbers, or observations. Handling data means organising, representing, and interpreting it to draw meaningful conclusions.
Collecting and Organising Data
Raw data is a list of observations collected directly. To make sense of it, we organise it using a tally mark system or a frequency table. A tally mark represents 5 as IIII (four verticals and one diagonal).
Frequency
The frequency of a value is how many times it appears in the data. A frequency distribution table shows each possible value and its frequency.
Pictograph
A pictograph uses pictures or symbols to represent data. Each symbol represents a fixed number. A key tells you the value of each symbol.
Bar Graph
A bar graph uses horizontal or vertical bars of equal width. The length of each bar represents the frequency or value. The bars do not touch each other (unlike a histogram for grouped data).
Data: heights of 10 students (cm): 140, 142, 140, 145, 142, 140, 143, 145, 142, 140.
Make a frequency table.
Height | Tally | Frequency
140 | IIII | 4
142 | III | 3
143 | I | 1
145 | II | 2
From the above table, what is the most common height?
140 cm appears most (4 times). This is called the mode.
Find the average (arithmetic mean) of: 8, 5, 12, 7, 3.
Mean = Sum / Count = (8+5+12+7+3) / 5 = 35 / 5 = 7.
A pictograph shows each symbol = 10 students. If Science has 4 symbols, how many students chose Science?
4 x 10 = 40 students.
The marks of 6 students are 45, 60, 55, 70, 65, 55. Find the mode and mean.
Mode = 55 (appears twice). Mean = (45+60+55+70+65+55)/6 = 350/6 ≈ 58.3.
A bar graph shows the number of books read per month: Jan=5, Feb=8, Mar=6, Apr=10, May=7. In which month were the most books read?
April — the bar for April is tallest (10 books).
The average weight of 4 people is 65 kg. A 5th person joins. The new average is 66 kg. What is the weight of the 5th person?
Old total = 4 x 65 = 260 kg. New total = 5 x 66 = 330 kg. 5th person = 330 - 260 = 70 kg.
- Key Terms
- Mean (Average): Sum of all values / number of values.
- Mode: The value that appears most often.
- Range: Largest value - Smallest value.
Common mistakes
- Forgetting that all bars in a bar graph must have the same width.
- Adding frequencies when finding the mean — mean = sum of values, not sum of frequencies.
- The mode is the most frequent value, not the highest value.
Summary
Data handling involves collecting, organising (tally/frequency tables), representing (pictographs, bar graphs), and interpreting data. Key statistical measures are mean (average), mode (most frequent), and range (spread).