Understanding Statistical Diagrams

 

What Are Statistical Diagrams?

Statistical diagrams are visual tools used to represent data. They help us:

• Spot trends and patterns
• Understand changes over time
• Make comparisons between groups
• Support decisions using data

Examples of statistical diagrams include:

• Bar charts
• Pie charts
• Line graphs
• Pictograms
• Time series graphs
• Cumulative frequency graphs

 

How Do I Interpret Them?

Step-by-step:

1. Read the context
   • What is the graph about?
   • Are there any units, dates, or descriptions?
   • What do the axes mean?
2. Check for a key
   • Are there colours, patterns, or line types explained?
   • Example: A dashed line for Year 8 and a solid line for Year 9
3. Read axis labels and scales carefully
   • Does the vertical axis start at zero?
   • Are numbers measured in 10s? 1000s? Millions?
4. Spot extreme values
   • These are called outliers
   • Ask: Is this value real or possibly an error?
5. Compare and calculate if needed
   • Use values from the graph to find mode, mean, median, or range
   • Look for changes and trends

 

How Do I Draw Conclusions?

Use specific language from the question. Your answer should:

• Refer to values from the graph
• Use units
• Mention the trend
• Include specific times or categories

Example:

"The number of books borrowed rose from 120 in January to 180 in March, an increase of 60 books over two months."

Avoid vague statements like:

"It went up."

 

When Not to Draw Conclusions

Sometimes the data isn’t reliable enough for strong conclusions. Be cautious if:

• The sample size is too small
• The data only covers part of the year
• There’s bias (e.g. only surveying people who already support something)

 

Example

A school tracks how many students walked or cycled to school over one week:

 

Day	Walked	Cycled
Monday	24	10
Tuesday	20	13
Wednesday	22	15
Thursday	18	12
Friday	26	16

 

(a) Describe the trend in students cycling to school

• Numbers increased from Monday (10) to Friday (16).
• Trend: Gradual rise in cyclists through the week.

(b) A teacher claims Thursday had the lowest overall active travel.

• Let’s check:
• Thursday: 18 (walked) + 12 (cycled) = 30
• Compare with other days:
  • Monday: 34, Tuesday: 33, Wednesday: 37, Friday: 42
• The teacher is correct — Thursday had the lowest total.

(c) Should the school use the mean or mode to describe cycling habits?

• Mean: (10 + 13 + 15 + 12 + 16) ÷ 5 = 13.2
• Mode: No mode (no repeating values)
• Use the mean — it gives a more reliable picture across the week.