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Unit 8 · Topic 01 · Data Handling

Organising Data: Bar Graphs, Range and Mean

Hook

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.

Watch the Lesson

The Story

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."

From tally to bar graphFootball 6Cricket 8Badminton 4
Football 6, Cricket 8, Badminton 4 — the tallest bar is the most popular.

So What Just Happened?

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.

Range and meanRange = largest - smallest = 15 - 8 = 7Mean = sum / count = 55 / 5 = 11
Ages 8, 12, 9, 15, 11: range = 15-8 = 7. Mean = 55/5 = 11.

Remember This

  • Organise raw data into a frequency table before trying to analyse it.
  • A bar graph's bar height equals the frequency (count) of that category.
  • Range = largest value minus smallest value.
  • Mean = sum of all values, divided by how many values there are.
  • The tallest bar in a bar graph shows the most common category at a glance.
Why organise data at allSee the pattern (bar graph); describe it (range, mean)
A bar graph shows the pattern; range and mean summarise it in one number each.

Try It Yourself

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.

Word Bank

Raw data
A list of individual observations, not yet organised or counted.
Frequency table
A table showing how many times each category or value occurs.
Bar graph
A chart with one bar per category, height equal to its frequency.
Range
The largest value in a data set minus the smallest value.
Mean
The sum of all values divided by how many values there are.

Questions

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