Practice Maths

L49 — Interpreting and Comparing Data

Key Ideas

Key Terms

range
The difference between the maximum and minimum values in a dataset. Range = max − min. Measures how spread out the data is.
outlier
A data value that is significantly higher or lower than most other values in the dataset. Outliers can have a large effect on the range.
cluster
A group of data values that are bunched close together in a particular range of the number line.
spread
How spread out or variable the data values are. A large range indicates high spread; a small range indicates consistency.
centre
The middle or typical value of a dataset — the area around which most values tend to cluster.
skewed
A dataset is skewed when values are bunched on one side, with fewer values forming a longer tail on the other side.

Describing and Comparing Datasets

When interpreting data, look for:

  • Centre: where most values sit (is the middle value high or low?)
  • Spread: how far apart the values are (use range: max − min)
  • Shape: is the data symmetric (balanced either side of centre) or skewed (bunched on one side)?
  • Outliers: values that sit far away from the rest of the data
  • Clusters: groups where values are bunched together
  • Gaps: ranges with no data values

When comparing two datasets, use structured language:

  • "Group A tends to have higher values than Group B."
  • "Group B has a wider spread — the range is ___ compared to Group A's range of ___."
  • "Both groups have a similar centre, but Group A is more consistent."
Hot Tip: Always refer to the actual data values and the context — avoid vague statements like "A is better" or "B is higher." Say how much higher and what that means in context.

Worked Example

Compare these two groups' test scores:

Group A: 55, 62, 68, 70, 71, 74, 75, 78

Group B: 40, 53, 65, 70, 72, 80, 83, 91

Three comparison statements:

  1. Group A has a range of 78 − 55 = 23, while Group B has a range of 91 − 40 = 51. Group B has a much wider spread.
  2. The middle values (median) of Group A (between 71 and 74 = 72.5) and Group B (between 70 and 72 = 71) are very similar — both groups performed at a similar level on average.
  3. Group A's scores are more consistent (clustered between 62 and 78), while Group B has both very low and very high scores, suggesting more varied ability.

Going Beyond "Reading" a Graph

Reading a graph means finding individual values — like "the temperature on Tuesday was 22 degrees." Interpreting a graph means going further and describing what those values tell you. You might notice a trend (the temperature rose steadily over the week), spot an unusual value (it dropped sharply on Thursday), or draw a conclusion (the data suggests it was a warm week overall). Strong interpretation uses specific values from the graph, not just vague statements.

What to Look for in a Single Dataset

When you look at any graph or data display, train yourself to notice five things:

Centre: Where are most of the values sitting — towards the lower end, the upper end, or the middle?

Spread: How wide is the range? A large range means the data is variable; a small range means the values are consistent.

Shape: Is the data roughly symmetric (balanced either side of the middle), or is it skewed to one side?

Outliers: Are there any values that sit far away from all the others? Outliers can be real events worth investigating, or they can be errors in data collection.

Clusters and gaps: Are there bunches of values in particular ranges, or stretches with no data at all?

Comparing Two Datasets

When you compare two groups, always comment on at least two things: their centres (which group tends to have higher or lower values?) and their spread (which group is more consistent?). Use specific numbers from the data. For example, "Group A has a range of 20, while Group B has a range of 45, so Group B's results are far more variable." Avoid vague comparisons like "Group A did better" — always say by how much and what that means.

A back-to-back stem-and-leaf plot or two dot plots side by side are great tools for comparing groups, because you can see both datasets in the same visual space.

Misleading Graphs

Not every graph gives an honest picture of the data. Watch out for these tricks: a y-axis that doesn't start at zero (making small differences look huge), bars of different widths, missing labels, or a scale that jumps unevenly. Always check the axis before interpreting any graph. If a graph makes one result look dramatically better or worse than another, check whether the scale is responsible.

Writing strong comparison sentences: A great comparison statement has three parts — what you are comparing, the actual values, and what it means in context. Example: "Class A has a median score of 72, which is 8 marks higher than Class B's median of 64, suggesting Class A performed better overall on this test." Try to follow this structure in every comparison you write.

  1. Comparing Pairs of Datasets

    For each pair of datasets, answer the four questions below.

    Pair 1 — Daily steps (thousands) for two friends over 8 days:

    Friend A: 7, 9, 8, 10, 7, 9, 8, 8

    Friend B: 3, 12, 6, 14, 5, 11, 4, 13

    Daily Steps — Friend A vs Friend B (thousands) A B 2 4 6 7 8 9 10 11 12 13 14 Steps (thousands)
    1. What is the range for each friend?
    2. What is the minimum and maximum for each friend?
    3. Which friend has more consistent step counts? How can you tell?
    4. Write one sentence comparing the two friends using range language.

    Pair 2 — Maths test scores (%) for two Year 7 classes:

    Class 7A: 45, 52, 58, 61, 65, 68, 71, 74, 78, 82

    Class 7B: 60, 62, 64, 66, 68, 70, 72, 74, 76, 78

    Maths Test Scores (%) — 7A vs 7B 7A 7B 45 52 58 61 65 68 71 74 78 82 Score (%)
    1. What is the range for each class?
    2. What is the lowest score in each class?
    3. Which class has a more even spread of scores?
    4. Write one sentence comparing the two classes.

    Pair 3 — Time (minutes) to complete a puzzle for two age groups:

    Adults: 8, 12, 9, 15, 11, 10, 14, 13, 9, 11

    Teenagers: 14, 18, 22, 17, 25, 16, 19, 21, 20, 15

    Puzzle Completion Time (min) — Adults vs Teenagers A T 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 Time (minutes)
    1. What is the range for each group?
    2. Compare the minimum times for adults and teenagers.
    3. Which group tends to complete the puzzle faster? Justify with data.
    4. Write a sentence comparing the two groups in context.

  2. Outliers, Shape & Spread

    1. Identify any outliers in this dataset of house prices ($000s): 320, 345, 310, 338, 355, 327, 315, 890, 342. Explain why this value is an outlier.
    2. Describe the shape of this dataset: 12, 13, 14, 14, 15, 15, 15, 16, 16, 17. Is it symmetric or skewed? Where are the values clustered?
    3. Two datasets each have 8 values. Dataset X has a range of 4; Dataset Y has a range of 30. What does this tell you about how spread out each dataset is?
    4. Look at this dataset: 5, 6, 7, 7, 8, 8, 8, 9, 9, 32. Without the outlier (32), the range is 4. With the outlier, the range is 27. What does this show about the effect of outliers on range?

  3. Are These Statements Supported by the Data?

    Use the data below to evaluate each statement as Supported, Not Supported, or Partly Supported. Explain your reasoning.

    Year 7 reading levels (books read per term): 3, 5, 4, 7, 2, 6, 5, 8, 4, 5

    Year 8 reading levels (books read per term): 6, 8, 7, 9, 5, 8, 10, 7, 6, 9

    1. "Year 8 students read more books per term than Year 7 students."
    2. "No Year 7 student read more than 8 books."
    3. "Year 7 has a wider variety of reading levels than Year 8."
    4. "All Year 8 students read at least 5 books per term."

  4. Write a Comparison & Draw Conclusions

    Two basketball players recorded their points scored across 10 games:

    Player 1: 8, 12, 15, 9, 11, 14, 10, 13, 12, 16

    Player 2: 4, 20, 8, 18, 5, 22, 7, 19, 6, 21

    Points per Game — Player 1 vs Player 2 P1 P2 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20 21 22 Points scored
    1. Calculate the range for each player.
    2. Find the minimum and maximum scores for each player.
    3. Write a comparison paragraph (3–4 sentences) describing the differences between the two players' performances, using data to support your statements.
    4. A coach needs to choose one player for a crucial final game where they need a reliable scorer. Which player should the coach choose, and why? Refer to both centre and spread in your answer.
    5. What are two limitations of comparing these players using only their range and min/max? What other information might be useful?

  5. Calculate range from a dataset

    For each dataset, find the minimum, maximum, and range.

    1. 14, 22, 9, 31, 17, 25
    2. 55, 62, 48, 70, 53, 67, 59
    3. 3, 3, 3, 7, 7, 7
    4. 0, 15, 30, 45, 60
    5. 101, 99, 105, 97, 103, 100
    6. 8, 8, 8, 8, 8

  6. Describe a single dataset

    The scores of 12 students on a science quiz are: 45, 52, 67, 71, 48, 55, 63, 70, 58, 49, 68, 72

    1. What is the range of scores?
    2. Identify any clusters — are the scores spread evenly, or bunched in a particular range?
    3. Are there any outliers? Explain how you decided.
    4. Write two sentences describing what the data tells you about how the class performed.

  7. Dot plots and comparison

    Two teams recorded the number of points scored per match over a season.

    Team Red: 5, 8, 6, 9, 7, 8, 7, 6, 8, 5

    Team Blue: 2, 11, 4, 13, 3, 12, 5, 10, 6, 14

    Points per Match — Team Red vs Team Blue R B 2 3 4 5 6 7 8 9 10 11 12 13 14 Points per match
    1. What is the range for each team?
    2. What is the minimum score for each team?
    3. What is the maximum score for each team?
    4. Which team has more consistent scores? How can you tell from the range?
    5. Both teams have the same total points. Does this mean they performed equally well? Explain.

  8. Comparing using a stem-and-leaf plot

    The back-to-back stem-and-leaf plot shows the weights (kg) of parcels sorted by two postal workers.

    Worker A (leaves) Stem Worker B (leaves)
    8   5   2 1 3   6   9
    9   7   4   1 2 0   2   5   8
    6   3 3 1   4
    5 4

    Key: Worker A: read right to left, e.g. 1 | 2 = 12 kg. Worker B: read left to right, e.g. 1 | 3 = 13 kg.

    1. List the weights for Worker A and Worker B separately, in order from lightest to heaviest.
    2. What is the range for each worker?
    3. How many parcels did each worker sort?
    4. Write two sentences comparing the parcel weights handled by each worker.

  9. Real-world data comparison

    A school canteen recorded daily sales ($) for two weeks:

    Week 1: $420, $385, $450, $310, $480

    Week 2: $395, $410, $425, $405, $415

    1. Calculate the range for each week.
    2. Find the minimum and maximum sales for each week.
    3. Which week had more consistent sales? Justify your answer using the range.
    4. On Monday of Week 1, sales were unusually low at $310. Explain why this might be considered an outlier in the context of the data.
    5. A school principal wants to know if sales are improving. What other information beyond range would you need to answer this question?

  10. Identify misleading conclusions

    Two students each walked 5 km during a school fundraiser. Their lap times (minutes) were:

    Student A: 6, 7, 6, 8, 7 min

    Student B: 4, 10, 5, 9, 6 min

    1. Both students have the same total time. Does this mean their performances were the same? Explain using range.
    2. Student B says "I had the fastest lap, so I am a better walker." Is this a fair conclusion? Explain.
    3. Which student was more reliable (consistent) in their pace? Justify with data.
    4. List one thing the range tells you about Student B's performance that it does not tell you about Student A.
    5. If you had to choose one student to represent the school in a long-distance race where a steady pace is important, which would you choose? Use the data to support your answer.
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