Data Handling and Presentation · Lesson 5 of 7
Applying and Checking Data Displays
“Use several kinds of displays together and spot when a graph disagrees with its data.”
• Recover a missing scale from a table and known bar heights. • Check every category in a graph against its source data. • Interpret a graph and test a proposed numerical comparison. • Organise new observations before choosing an appropriate display. • Suggest ways to investigate explanations for a visible pattern.
Recover and repair a partial graph
Imagine a railway-ticket bar graph with erased values on its axis. The table says Vidisha sold 24 tickets and Jabalpur 20; their bars measure six and five equal units. Both tell us that one unit means four tickets, because 24 ÷ 6 = 4 and 20 ÷ 5 = 4. We can restore the labelled scale, add the missing Sagar bar, and check the other bars.
| City | Vidisha | Jabalpur | Seoni | Indore | Sagar |
|---|---|---|---|---|---|
| Tickets | 24 | 20 | 16 | 28 | 16 |
| Height at 4 tickets per unit | 6 | 5 | 4 | 7 | 4 |
Problem
The Vidisha bar is 6 units for 24 tickets. How tall should the Indore and Sagar bars be?
- 1.First find the key: 24 ÷ 6 = 4 tickets per unit. Confirm using Jabalpur: 20 ÷ 5 = 4.
- 2.Indore sold 28 tickets, so its bar must be 28 ÷ 4 = 7 units. Sagar sold 16, so its bar must be 16 ÷ 4 = 4 units.
- 3.Label the numbered axis 0, 4, 8, … in equal intervals and check Seoni, which also needs a four-unit bar. Correct an Indore bar if it differs.
A graph can have a valid scale and still contain a wrongly drawn bar. Recalculate each bar from the table, and look for missing or mismatched categories as well as incorrect tick labels.
Move between collection, tables, and graphs
The chapter’s transport survey begins as an unsorted list of vehicles observed in one hour. Before drawing a pictograph or bar graph, tally each vehicle type and check the total. Its counts are bike 13, car 6, bicycle 8, auto rickshaw 8, scooter 9, bus 4, and bullock cart 2, totalling 50 observations. A second observer should use the same category names and recording rule to make the work comparable.
| Vehicle | Bike | Car | Bicycle | Auto rickshaw | Scooter | Bus | Bullock cart |
|---|---|---|---|---|---|---|---|
| Frequency | 13 | 6 | 8 | 8 | 9 | 4 | 2 |
Rolling a die 30 times gives another frequency table; the six results must total 30, even though we cannot predict which face will be most frequent. A wickets table calls for a different question: 30 matches is the sum of its frequencies, while 90 wickets is the sum of each wickets-per-match value multiplied by its frequency. State which quantity is being asked for before combining numbers.
Interpret, check, and investigate
A bar graph of saplings planted on Monday through Sunday allows students to add the Wednesday and Thursday counts (70) and the whole week (310), then identify Saturday as the highest day and Wednesday as the lowest. Rain or attendance may be possible reasons for the pattern; the graph does not establish either. Checking rainfall records or attendance on those days would provide further evidence.
A free-time survey of 120 students records 45 for playing, 30 for reading story books, 20 for watching TV, 10 for listening to music, and 15 for painting. All five counts total 120. With five students per unit, the bars have heights 9, 6, 4, 2, and 3 units. Reading story books is the most popular activity other than playing.
Problem
Use five students per unit for the activity counts 45, 30, 20, 10, and 15. Which activity comes second?
- 1.Divide each count by 5: playing 9 units, reading 6, watching TV 4, listening to music 2, and painting 3.
- 2.The tallest bar is playing at 9 units; reading is next at 6 units.
- 3.Check the original table: 30 reading responses are more than the other non-playing categories. Label both the key and every category.
| Year | 2006 | 2010 | 2014 | 2018 | 2022 |
|---|---|---|---|---|---|
| Approximate tigers in India | 1,400 | 1,700 | 2,200 | 3,000 | 3,700 |
Problem
How can you check a horizontal graph against the five tiger counts?
- 1.Read its scale from zero and translate each bar length back to a count, allowing only the precision indicated by the graph.
- 2.Compare the recovered values with 1,400, 1,700, 2,200, 3,000, and 3,700, one year at a time.
- 3.The displayed graph has incorrect bars for 2006, 2010, 2014, and 2018. Redraw those to match the table; preserve the correctly placed 2022 value. Note that these numbers are approximate estimates.
The tractor and girl-student pictographs and the Mudhol Hounds construction question give similar opportunities to check a key, compare counts, and explain a half symbol. Those tasks were introduced with pictographs; here they can be used alongside a table or bar graph to ask whether both displays convey the same quantities.
Quiz
A bar of 6 units represents 24 tickets. One unit represents…
At four tickets per unit, what height shows 28 tickets?
The vehicle counts 13, 6, 8, 8, 9, 4, 2 should sum to…
With five students per unit, the reading story books count of 30 needs a bar of…
Which statement about the saplings graph is supported without another investigation?
What is the right first step when checking a tiger bar graph?
Practice Problems
- Restore the ticket graph’s scale from Vidisha’s 24 tickets in 6 units, then find the correct heights for all five cities.
- A ticket graph shows Indore at only five units with four tickets per unit. Explain the error and give the repaired height.
- Tally a short roadside observation yourself. Make a table, check the total, and explain which graph you would use.
- For the free-time survey, verify the total of 120 and give all five bar heights on the specified five-student scale.
- Compare the tiger table with a classmate’s drawn graph. Check the axis and each year’s bar, recording every disagreement.
- A weekly saplings graph shows fewer plants on Wednesday. Give two possible explanations and one observation that could help test each.
- Using the village dog counts 18, 36, 12, 48, 18, 24, compare villages B and D together with the other four by calculation.
Key Takeaways
• Use the same scale to check every bar against its table value. • An erased scale can sometimes be recovered by dividing a known value by its bar height. • Keep track of what is being counted when adding frequencies or finding totals of values. • Graphs show patterns; investigate further before claiming what caused them.