Unit 8 · Topic 01 · Data Handling
Ms. Rao handed Kabir a messy list of 20 students' shoe sizes, scribbled in the order they were measured.
Kabir stared at the jumble, unable to say anything useful about it at a glance.
Anaya turned the same list into a bar graph, and suddenly three questions were answered in one look.
Ms. Rao gave the class a raw list: 20 students' favourite sports, written down exactly in the order each student answered — Football, Cricket, Football, Badminton, Cricket, Football, Cricket, Cricket, Badminton, Football, and so on. "What's the most popular sport?" she asked. Kabir stared at the jumbled list, trying to keep a running count in his head and losing track twice.
Anaya took a different approach. She made a tally: Football ||||, Cricket |||||, Badminton ||. "Now count the tally marks," she said. "Cricket: 8. Football: 6. Badminton: 4. Wait, that's only 18 — let me recheck two entries." She fixed her count and confirmed the totals matched all 20 students.
"Once the data is organised into a frequency table like this," said Ms. Rao, "you can draw a BAR GRAPH — one bar per category, with height equal to its count. Now the most popular sport is obvious: whichever bar is tallest, Cricket."
Ms. Rao then gave a second, numeric example: the ages of 5 cousins — 8, 12, 9, 15, 11. "What's the RANGE of these ages?" Anaya answered immediately: "Range is the biggest value minus the smallest: 15 minus 8 is 7." "And the MEAN?" Anaya added all five ages — 8+12+9+15+11=55 — then divided by how many there were, 5, giving a mean of 11.
"So organising raw data does two things," Anaya summarised. "A bar graph lets you SEE the pattern at a glance — tallest bar, most common category. And numbers like range and mean let you DESCRIBE the spread and the typical value with a single number each, instead of staring at a long jumbled list."
Raw data (a list of individual observations, in no particular order) becomes much easier to understand once it is organised into a FREQUENCY TABLE — a count of how many times each category or value occurs.
A BAR GRAPH represents a frequency table visually: one bar per category, with the bar's height equal to its frequency (count). The tallest bar shows the most common category at a glance.
The RANGE of a set of numeric values is the largest value minus the smallest value — it describes how spread out the data is.
The MEAN (average) of a set of numeric values is the sum of all the values, divided by how many values there are — it describes a single typical value representing the whole set.
Ask 10 classmates their favourite colour, tally the results, and draw a simple bar graph.
Find the range and mean of these 6 test scores: 14, 18, 12, 20, 16, 15.
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