Histograms
Frequency Distribution · Level 5 Statistics
Ngā Whāinga Akoranga · Learning Intentions
- Create and interpret histograms from grouped (continuous) data
- Understand frequency distribution and class intervals
- Identify the modal class and describe the shape of a distribution
- Distinguish histograms from bar graphs and explain when each is appropriate
Paearu Angitu · Success Criteria
- I can correctly draw a histogram with touching bars and labelled axes
- I can identify the modal class from a histogram or frequency table
- I can calculate a percentage from frequency data (e.g. "what % scored above 60?")
- I can describe a distribution as normal, skewed left, or skewed right
Hononga Marautanga · Curriculum Alignment
Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.
Whakataukī
"He aha te mea nui o te ao? He tāngata, he tāngata, he tāngata"
What is the greatest thing in the world? It is people, it is people, it is people.
Histograms help us understand groups of people — their ages, heights, and achievements. Like our tīpuna who understood the distribution of resources across seasons, we use histograms to see how data is distributed across ranges.
Histogram vs Bar Graph
- Continuous data (ranges/intervals)
- Bars touch — no gaps
- Shows frequency distribution
- e.g. height ranges, test score ranges
- Categorical data (separate groups)
- Bars have gaps between them
- Compares different categories
- e.g. favourite sports, types of pets
Modal class = the class interval with the highest frequency — the tallest bar on the histogram.
Histogrāma 1 · Year 10 Maths Test Scores (50 students)
| Score range | Frequency (students) | Percentage of class |
|---|---|---|
| 0–20 | 2 | |
| 21–40 | 5 | |
| 41–60 | 12 | |
| 61–80 | 20 | |
| 81–100 | 11 | |
| Total | 50 | 100% |
Draw your histogram below. Bars must touch. Label the X-axis (score range) and Y-axis (frequency). Title your histogram.
1. Fill in the percentage column above. Show one calculation.
2. Which score range is the modal class? How many students scored in that range?
3. How many students scored above 60%? What percentage of the class is that?
4. Describe the shape of this distribution: normal (symmetric), skewed left, or skewed right? Explain.
Histogrāma 2 · Student Commute Times to School (200 students)
| Travel time (min) | Frequency (students) | Percentage of total |
|---|---|---|
| 0–10 | 85 | |
| 11–20 | 60 | |
| 21–30 | 35 | |
| 31–40 | 15 | |
| 41–50 | 5 | |
| Total | 200 | 100% |
1. What is the modal class (most common travel time range)?
2. How many students travel for more than 20 minutes?
3. What percentage of students have a commute of 10 minutes or less? Show working.
4. Describe the shape of this distribution. Is it skewed? Which direction? Why does this make sense given what the data represents?
Histogrāma 3 · Create Your Own
Collect height data from your class (to the nearest 5 cm). Record in the frequency table, calculate percentages, then draw the histogram.
| Height range (cm) | Tally | Frequency | Percentage |
|---|---|---|---|
| 140–149 | |||
| 150–159 | |||
| 160–169 | |||
| 170–179 | |||
| 180–189 | |||
| Total | 100% |
What does your histogram tell you about the height distribution in your class? What is the modal class?
Aronga Mātauranga Māori
The phrase "He tāngata, he tāngata, he tāngata" reminds us that understanding people — their patterns, their distributions, their resilience — is at the heart of all meaningful knowledge. Histograms of demographic data (age structures, educational outcomes, housing density) reveal social realities. Māori demographic data — including the remarkable population recovery from ~42,000 in 1896 to over 875,000 today — tells a story of extraordinary resilience.
When Te Puni Kōkiri or iwi present data about Māori educational achievement or health outcomes, they use distributions. Understanding what a skewed distribution means — and what it implies about systemic barriers — is a form of statistical literacy that supports advocacy for equity.
Ngā Rauemi Tautoko · Support Materials
Resources already provided:
- This handout with frequency tables and graph-drawing grids
- Ruler — essential for drawing histogram bars with straight edges
- Calculator (permitted for percentage calculations)
- Coloured pencils — use different colours for different histograms
Aronga Rerekē · Differentiated Pathways
Tīmata · Entry Level
Complete Histogram 1. Draw the bars using the frequency table (don't need to calculate percentages). Answer questions 2 and 3 only.
Paerewa · On Level
Complete Histograms 1 and 2 fully including percentage columns. Answer all questions. Draw Histogram 3 if time allows.
Tūāpae · Extension
Complete all sections. Look up a real NZ dataset (Stats NZ or NIWA) and create a histogram of your own choosing. Write a paragraph explaining what the distribution tells us about that aspect of NZ society or environment.