Grade 8 · Unit 4: Showing data¶

Track: A (no-code); optional CODAP · Tools: graph paper, optional CODAP · Lessons: 3 Datasets: class-survey-synthetic, census-districts

Big idea. A graph is an argument made visible. The right graph helps the eye; a careless one can mislead.

What you will be able to do

I can draw a bar chart, dot plot and line graph from a table.
I can choose a graph that fits the data.
I can spot a misleading graph.

Words to know: bar chart (स्तम्भचित्र), pie chart (वृत्तचित्र), dot plot (बिन्दुचित्र), histogram (आयतचित्र), line graph (रेखाचित्र), axis, scale, title. Full list: curriculum/framework/glossary.md.

Before you start¶

From Unit 3: frequency tables (counts per category), grouped frequency tables for numbers, and the tidy class table. From Unit 1: numerical vs categorical. The type of variable decides the type of graph.

Lesson 1: Bar charts and dot plots¶

Hook (5 min). Here are 20 travel times in minutes: 53, 27, 40, 23, 11, 48, 21, 7, 12, 52, 10, 41, 27, 54, 32, 10, 5, 35, 42, 19. Without drawing anything, what is a typical time? Now look at the dot plot your teacher draws. Which was easier?

Explanation¶

Our eyes are excellent at comparing lengths and positions, and poor at comparing long lists of numbers. A graph turns numbers into lengths and positions.

Bar chart — for a categorical variable. One bar per category; the length shows the count (or a value such as population). Rules: * bars have equal width and gaps between them (the categories are separate); * the value axis starts at zero, because the eye compares whole bar lengths; * order bars in a useful way: largest to smallest, or a natural order (Mountain, Hill, Terai).

Dot plot — for a numerical variable with a small number of cases (up to about 50). Draw a number line, then put one dot for each case above its value; stack dots that land on the same value. A dot plot shows: * where values cluster (most students take 20–45 minutes), * gaps and unusual values (one student takes 90 minutes?), * the spread from smallest to largest.

Histogram — for a numerical variable with many cases. Use the grouped frequency table from Unit 3: one bar per class, bars touching (because the number line is continuous), height = frequency. Think of it as a dot plot where dots are piled into class "buckets".

Worked example. From the 36-student class table:

Travel mode (bar chart, counts)
walk       ██████████████████████████  26
bus        █████                        5
bicycle    ███                          3
motorbike  ██                           2
           0    5    10   15   20   25

Travel minutes (histogram, classes of 10 minutes)
 9 |         ██
 8 |         ██
 7 |     ██  ██  ██  ██
 6 |     ██  ██  ██  ██
 5 |     ██  ██  ██  ██
 4 |     ██  ██  ██  ██  ██
 3 |     ██  ██  ██  ██  ██
 2 | ██  ██  ██  ██  ██  ██
 1 | ██  ██  ██  ██  ██  ██
   +------------------------
     0-  10- 20- 30- 40- 50-

The histogram shows travel times spread quite evenly from 10 to 50 minutes, with few very short or very long trips.

Every graph needs: a title that says what and where/when, labelled axes with units, a sensible scale with equal steps, and the data source.

Activity (20 min)¶

On graph paper, draw a bar chart of travel_mode from your class table (or the frequency table in Unit 3).
Draw a dot plot of travel_minutes: number line from 0 to 60, one dot per student.
Write two sentences about the dot plot: where most values are, and anything unusual.
CODAP version: drag the class CSV into CODAP, make a graph, drag travel_mode to the x-axis (bar chart), then travel_minutes (dot plot). Try the "fuse dots into bars" option to get a histogram.

Common mistakes¶

Using a bar chart for a numerical variable with many values (one bar per student is not a summary).
Bars of different widths, or a value axis that does not start at zero.
No units on the axis ("time" — seconds? minutes? hours?).

Check (5 min). 1. Which graph suits 'favourite subject'? 2. What can a dot plot show that a table hides? 3. What must every graph have?

Reflect (2 min). What surprised me? Who or what is missing from this data?

Lesson 2: Line graphs and pie charts¶

Hook (5 min). You have (a) the temperature at noon each day for a week and (b) the share of students who walk, bus and cycle. Which graph fits each? Predict before the lesson.

Explanation¶

Line graph — for change over time. Time goes on the horizontal axis, in order and with equal spacing (if a year is missing, leave a gap; do not squeeze the axis). Points are joined because the time between them is continuous. Line graphs show trends (going up, going down) and seasons (repeating patterns).

Worked example with real data. Our World in Data (RD-02) reports the share of children in Nepal who die before their fifth birthday:

Year	1960	1970	1980	1990	2000	2010	2020
Child mortality (%)	33.0	26.8	20.8	13.8	7.9	4.8	3.0

Source: Our World in Data, child-mortality chart (UN IGME estimates), downloaded 2026-10-11.

Plotted as a line graph (years on the x-axis, percent on the y-axis from 0 to 35), it shows one of the most important stories in Nepal's history: in 1960 about one child in three died before age five; by 2020 about one in 33. Asking why (vaccination, clean water, health posts, mothers' education) is how data lead to real questions.

Pie chart — for parts of one whole, when the parts add to 100%. Each slice's angle is its share of 360°:

angle = (frequency ÷ total) × 360°

For the class table: walk 26/36 × 360° = 260°, bus 5/36 × 360° = 50°, bicycle 3/36 × 360° = 30°, motorbike 2/36 × 360° = 20°. Check: 260 + 50 + 30 + 20 = 360°.

Pie charts work only with a few categories (up to about 5) and when the "whole" makes sense. A bar chart is almost always easier to read, because comparing angles is hard for the eye. Use a pie when the message is "this is most of the whole".

Activity (20 min)¶

Draw a line graph of the child-mortality table above. Use a y-axis from 0 to 35 with steps of 5.
Describe the trend in one sentence. In which decade did the percentage fall the most?
Convert the class travel-mode frequencies to angles and draw a pie chart with a protractor. Label each slice with its percent.
Discuss: would a bar chart or the pie chart show the travel data better? Why?

Common mistakes¶

A pie chart for values that are not parts of one whole (e.g. "minutes for each student").
Joining points with lines when the x-axis is categories, not time (provinces in a line graph).
Uneven time spacing (1960, 1990, 2000, 2020 equally spaced on the axis).

Check (5 min). 1. Which graph shows change over days? 2. Walk 12, bus 5, cycle 3 of 20: percent who walk? 3. Why would a pie chart of 'minutes by student' be wrong?

Reflect (2 min). What surprised me? Who or what is missing from this data?

Lesson 3: Misleading graphs¶

Hook (5 min). A newspaper bar chart shows Ward A's bar five times taller than Ward B's. The numbers are 52 and 50 households with taps. How is that possible?

Explanation¶

A graph can be accurate and still give a false impression. The most common tricks:

Trick	What happens	How to catch it
Truncated axis	The y-axis starts at 48, so 52 vs 50 looks like 4 vs 2	Read where the axis starts
Uneven scale	Steps of 10, then 50, then 100	Check the spacing of the numbers
3D and pictures	A coin drawn twice as tall is also twice as wide: it looks 4 times bigger	Compare numbers, not areas
Cherry-picking	Showing only the years where the line goes up	Ask what happened before and after
Missing context	"Cases doubled!" from 2 to 4	Ask "out of how many?"
Two y-axes	Two lines on different scales seem to move together	Read both axes
Claim beyond the data	Title says "Our school is the best" from a chart of 3 schools	Compare the title with what is plotted

When is a non-zero axis fine? For line graphs of things that never get near zero (body temperature, exchange rate), starting at a sensible value shows the change better. For bar charts, always start at zero, because bar length is the message.

Worked example. The heights of the bars in the hook: * With the axis starting at 48: Ward A bar = 52 − 48 = 4 units, Ward B bar = 50 − 48 = 2 units → looks 2 times bigger. (If it started at 49.5, it would look 2.5 ÷ 0.5 = 5 times bigger.) * With the axis starting at 0: 52 vs 50 → Ward A is only 4% bigger.

Activity (20 min)¶

Your teacher shows four "bad" graphs (from newspapers, social media or drawn on the board).
In groups, for each graph: name the trick, say what impression it gives, and what the honest message is.
Redraw one graph honestly on graph paper.
Challenge: draw a deliberately misleading graph of the class travel data, then swap with another group who must find your trick.

Common mistakes¶

Reading the shape of a graph before reading its axes.
Thinking every non-zero axis is cheating (fine for line graphs of values far from zero, never for bars).
Trusting a graph because it looks professional.

Check (5 min). 1. Axis starts at 48 instead of 0 — effect? 2. Name one more way to mislead with a graph. 3. What is the first thing you check on a graph?

Reflect (2 min). What surprised me? Who or what is missing from this data?

Unit summary¶

Categorical → bar chart (or pie for parts of a whole). Numerical → dot plot (small data) or histogram (many values). Change over time → line graph.
Every graph needs a title, labelled axes with units, equal scale steps and a source.
Bar charts start at zero; histogram bars touch; time axes are evenly spaced.
Pie slice angle = share × 360°.
Read the axes first: truncated axes, uneven scales, 3D, cherry-picking and missing context all mislead.

Practice exercises¶

★ Name the best graph: (a) number of students by favourite festival, (b) monthly rainfall in Pokhara over a year, (c) heights of 30 students, (d) share of Nepal's population in Mountain, Hill and Terai.
★ Why do histogram bars touch but bar-chart bars do not?
★ Favourite subjects: Maths 12, Social 11, Nepali 6, Science 5, English 2. Draw a bar chart in order from largest to smallest.
★★ Work out the pie-chart angles for exercise 3. Check that they add to 360°.
★★ Draw a dot plot of these sleep hours (round to the nearest half hour first): 8.2, 6.7, 7.1, 8.1, 8.6, 6.7, 8.7, 6.6, 7.2, 8.9, 9.7, 7.9. Describe what you see.
★★ Using the child-mortality table, by how many percentage points did child mortality fall from 1990 to 2010? By what fraction did it fall (from 13.8 to 4.8)?
★★ A chart shows enrolment rising from 980 to 1,000 with the y-axis from 970 to 1,000. Describe the impression, then redraw it honestly.
★★★ A poster shows two bags of rice, one drawn twice as tall as the other, to show that the price doubled. Why does this exaggerate the change?
★★★ The synthetic district table gives population by ecological belt: Mountain 1,060,048, Hill 11,907,289, Terai 14,366,042. Choose a graph and draw it. Explain your choice. (Remember: this table is synthetic.)
★★★ Find a graph in a newspaper or on social media. Stick or sketch it in your notebook and write a three-line review: what it shows, one strength, one problem.

Exercises with real data¶

R1. Tourists over time (RD-10). Use the Open Data Nepal tourist arrivals table (2001–2014). Draw a line graph of total arrivals by year. Mark any year where arrivals fell, and write one question about why (look up events of that year). Draw a second line for arrivals by air: is most tourism by air or by land? Offline fallback: line graph of mean_temp_c for the 12 months of one year in climate_monthly_synthetic.csv.

R2. South Asia's children (RD-02). From the Our World in Data child-mortality chart, copy the values for Nepal, India, Bangladesh and Sri Lanka for 1990 and 2020 (or use the table in Lesson 2 for Nepal). Draw a grouped bar chart (two bars per country). Which country has always had the lowest rate? Which improved most between 1990 and 2020?

R3. Earthquake magnitudes (RD-05). Use the grouped frequency table you made in Unit 3, exercise R1, to draw a histogram. Describe its shape: where is the tallest bar, and which side has a long "tail"?

Unit project: Graph gallery¶

Follow Problem · Plan · Data · Analysis · Conclusion. Make four graphs of your class data (one bar chart, one dot plot or histogram, one pie chart, one line graph of something measured over a week), each with a title, axes, units and a one-sentence message, plus one deliberately misleading graph with a note explaining the trick. Display them as a gallery walk. Full brief and rubric: project.md.

If you use an AI assistant, follow the AI-use policy (explain, don't answer; disclose; be ready for an oral check).

Going further¶

Our World in Data, https://ourworldindata.org/country/nepal: dozens of line graphs about Nepal; pick one and explain it to your family.
Darrell Huff, How to Lie with Statistics (1954): a short, funny, classic book on misleading graphs and numbers.