Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Data Representation.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
Data representation is the process of organizing and displaying data using charts, graphs, or tables so that patterns, trends, and comparisons become easier to see and understand at a glance.
Raw data is like puzzle pieces scattered on a table - hard to make sense of. When you organize it into charts, graphs, or tables, the picture becomes clear. A bar chart of ice cream preferences instantly shows which flavor wins, while a list of 100 names wouldn't.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Data Representation organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to data representation but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
medium
A bar graph shows 4 categories with mean 12. If three bars are 9, 14, and 10, what is the fourth bar?The mean of all four bars is 12. What is the value of the fourth bar?
Answer
15
First step
1
Sum required =12×4=48.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A pie chart shows red 25%, blue 40%, green g%, yellow 15%. Find g.Red is 25%, Blue is 40%, Yellow is 15%. What percent is Green?
Example 3
challenge
A pictograph designer must choose a key value k so that categories with counts 24, 36, and 60 each use a whole number of symbols. What is the largest such k?
Example 4
easy
A class recorded the number of pets owned by each student: 0, 1, 1, 2, 3, 1, 0, 2, 4, 1. Organise this data into a frequency table.
Example 5
easy
Which type of graph would be most appropriate to display the favourite ice-cream flavours of 30 students: a bar graph, a line graph, or a scatter plot? Explain.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A bar graph shows bars of heights 5, 8, 3. What is the total represented?What is the total represented by all three bars?
Example 2
easy
Which display best shows categorical data: a bar graph or a number line? Answer 1 for bar graph, 2 for number line.
Example 3
easy
A pictograph key says one symbol = 4. There are 3 symbols. How many items total?
Example 4
easy
A table lists counts 2, 4, 6, 8. What is the largest value shown?
Example 5
easy
Two bars show 7 and 10. How much taller is the second bar?How much taller is the second bar than the first?
Example 6
easy
A display should always have its axes labeled. If a graph has 0 labeled axes out of 2, how many labels are missing?
Example 7
easy
A frequency table has categories with counts 3, 3, 3, 3. What is the total?
Example 8
easy
To compare 4 categories quickly, which is clearer: a labeled bar graph or an unsorted list? Answer 1 for bar graph, 2 for list.
Example 9
medium
A pictograph uses a key of 1 symbol = 5. A row has 4 full symbols and 1 half symbol. How many items does the row show?
Example 10
medium
A bar graph shows categories 8, 6, 10, 4. What is the average (mean) bar height?What is the mean (average) bar height?
Example 11
medium
A pictograph key is 1 symbol = 6. A category has 30 items. How many symbols are drawn?
Example 12
medium
A frequency table shows counts 12, 9, 6. To draw a bar graph, what scale interval evenly fits all three with the fewest gridlines, using a step that divides all? Give the largest such step.
Example 13
medium
A display shows 5 categories. If 2 categories are each 10 and the other 3 are each 4, what is the grand total?
Example 14
medium
A pictograph row shows 7 symbols where each = 3. A second row shows 5 symbols of the same key. How many more items are in the first row?
Example 15
challenge
A misleading bar graph starts the axis at 20 instead of 0. Two bars reach 50 and 60. The true ratio of values is what, as a simplified fraction (smaller to larger)?
Example 16
challenge
A pictograph must show 27 items with a key where each symbol = 4. How many full symbols and what fraction of a symbol are needed? Give the fraction part.
Example 17
challenge
A bar graph and pictograph show the same data of 48 items. The bar graph uses a step of 8 per gridline; the pictograph uses a key of 6 per symbol. How many more gridlines than symbols are used to reach 48?
Example 18
medium
A pictograph key is 1 symbol = 7. A category has 49 items. How many symbols are drawn?
Example 19
medium
A bar graph shows heights 4, 8, 12. To pick a scale step dividing all evenly, give the largest such step.What is the largest step size that divides all three bar heights evenly?
Example 20
medium
A display has 6 categories: 3 are each 5 and 3 are each 9. What is the grand total?
Example 21
easy
A bar graph shows bars of heights 4, 6, 9, 2. What is the total represented?What is the total represented by all four bars?
Example 22
easy
Which display best shows numerical data spread over a range: a dot plot or a pie chart of categories? Answer 1 for dot plot, 2 for pie chart.
Example 23
easy
A pictograph key says one symbol = 3. There are 7 symbols. How many items total?
Example 24
easy
A table lists counts 9, 4, 7, 2, 6. What is the smallest value shown?
Example 25
easy
Two bars show 12 and 5. How much taller is the first bar than the second?How much taller is the first bar than the second?
Example 26
easy
A frequency table has counts 5, 5, 5, 5, 5. What is the total?
Example 27
easy
To show change over time, which is more appropriate: a line graph or a pie chart? Answer 1 for line graph, 2 for pie chart.
Example 28
medium
A pictograph uses a key of 1 symbol = 4. A row has 6 full symbols and 1 quarter symbol. How many items does the row show?
Example 29
medium
A bar graph shows categories 9, 5, 11, 7, 8. What is the mean (average) bar height?What is the mean (average) bar height?
Example 30
medium
A pictograph key is 1 symbol = 8. A category has 56 items. How many symbols are drawn?
Example 31
medium
A frequency table shows counts 18, 12, 24. What scale step (the largest whole number that divides all three) lets bar tops sit exactly on gridlines?
Example 32
medium
A line graph shows temperatures 60, 64, 70, 68, 72 over five days. By how much did the temperature increase from day 1 to day 5?By how much did the temperature increase from day 1 to day 5?
Example 33
medium
A pictograph uses 1 symbol = 5 books. The library row shows 3.5 symbols. How many books does the row represent?
Example 34
hard
A bar graph using y-axis ticks of 5 starts at 0. Bars are at heights 17, 23, 8, 12. How many bars land exactly on a gridline?
Example 35
hard
A line graph runs from 0 to 100 on the y-axis with 5 evenly spaced gridlines after 0. What value does each gridline step represent?
Example 36
hard
A bar graph shows 5 categories with mean 14 and total 70. If the largest bar is 22 and the smallest is 6, what is the sum of the other three bars?
Example 37
hard
A pictograph uses 1 symbol = 12. To show 78 items, how many full symbols plus what fraction of a symbol is needed? Give the fraction part.
Example 38
medium
A dot plot has dots at values 3, 4, 4, 5, 6, 6, 6. How many dots are on value 6?
Example 39
challenge
A bar graph uses a y-axis step of 4. Bars must end on gridlines. Among heights 12, 16, 22, 28, how many bars CANNOT end exactly on a gridline?
Example 40
easy
A student collected data on daily high temperatures (in °C) over two weeks. Should they use a bar graph or a line graph to display this data? Justify your answer.
Example 41
easy
A cafeteria records the number of sandwiches sold each day for six weeks. Which display would best show the overall trend over time: a line graph, a bar graph, or a pie chart? Explain.