Practice Maths

Univariate Data Analysis — Topic Review

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15 questions covering all Univariate Data sub-topics: data classification, displays, measures of centre, measures of spread, normal distribution and z-scores, and comparing data sets.

  1. Fluency

    Classify each of the following as categorical (nominal or ordinal) or numerical (discrete or continuous):

    1. Eye colour
    2. Number of siblings
    3. Height in centimetres
    4. Movie rating (G / PG / M / MA)
  2. Fluency

    Find the mean, median and mode of: 6, 9, 4, 9, 7, 3, 9, 8, 5, 10

  3. Fluency

    Find Q1, Q3 and IQR for: 8, 12, 15, 18, 22, 26, 30, 35

  4. Fluency

    Heights follow a normal distribution: μ = 175 cm, σ = 8 cm. Find the z-score for a height of 191 cm.

  5. Fluency

    A normal distribution has μ = 50, σ = 5. What percentage of values lie between 40 and 60?

  6. Understanding

    Dataset: 14, 17, 19, 21, 23, 25, 27, 62. Use the IQR outlier method to determine whether 62 is an outlier. Show all working.

  7. Understanding

    Two datasets have mean = 25. Dataset A has SD = 3, Dataset B has SD = 10. Describe what each standard deviation tells you about the spread of each dataset.

  8. Understanding

    Biology test: μ = 60, σ = 12. Chemistry test: μ = 72, σ = 15. Sam scored 78 on Biology and 90 on Chemistry. In which test did Sam perform better relative to the rest of the class? Use z-scores.

  9. Understanding

    A box plot has: Min = 5, Q1 = 12, Median = 18, Q3 = 26, Max = 34.

    1. Find the IQR.
    2. Use the fence test to check for outliers.
    3. Describe the shape of the distribution.
  10. Understanding

    Pulse rates (bpm): Athletes: 52, 58, 60, 62, 65, 68, 70. Non-athletes: 68, 72, 75, 78, 80, 82, 88. Find the median and IQR for each group. Compare the centre and spread.

  11. Understanding

    In a normal distribution, what percentage of data lies: (a) above μ + 2σ? (b) below μ − σ? (c) between μ and μ + σ?

  12. Problem Solving

    Exam scores for two classes:
    Class 1: 45, 52, 61, 68, 74, 78, 82, 89
    Class 2: 38, 55, 66, 70, 72, 75, 83, 91
    Calculate mean, median and IQR for each class. Compare using shape, centre and spread. Which class performed better overall?

  13. Problem Solving

    Weekly wages ($): 520, 540, 560, 580, 600, 620, 650, 2400.

    1. Calculate the mean and median.
    2. Which measure better represents a ‘typical’ wage? Explain.
    3. Calculate the IQR and use the fence test to determine if $2400 is an outlier.
  14. Problem Solving

    Heights follow a normal distribution: μ = 170 cm, σ = 10 cm.

    1. What percentage of people are between 150 cm and 190 cm?
    2. What percentage are taller than 190 cm?
    3. In a group of 500 people, how many would you expect to be shorter than 150 cm?
  15. Problem Solving

    A researcher records data for 8 students: study hours per week (x): 2, 3, 3, 4, 5, 6, 6, 7, and corresponding test scores (%): 55, 62, 65, 70, 74, 80, 78, 85.

    1. Calculate the mean study hours and mean test score.
    2. Describe the shape of the test score distribution (use mean vs median).
    3. Does the data appear to support a claim that more study leads to higher scores? Comment using the data.
    4. What further statistical analysis would be needed to confirm this relationship?
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