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Chapter 2 Homework — Multiple Choice

Descriptive Statistics — 20 multiple-choice questions covering histograms, measures of location, measures of center, skewness, spread, and z-scores.

Choose the single best answer for each question.

2.2 — Histograms and Shape

  1. 1.

    A histogram has most of the data piled near the low end and a long tail extending to the right. The shape is best described as:

    1. A.Symmetric
    2. B.Right-skewed (positively skewed)
    3. C.Left-skewed (negatively skewed)
    4. D.Bimodal
  2. 2.

    A relative frequency histogram differs from an ordinary frequency histogram in that:

    1. A.The horizontal scale shows percentages instead of data values
    2. B.The vertical scale shows proportions or percentages instead of counts
    3. C.The bars do not have to touch
    4. D.There is no real difference
  3. 3.

    A histogram of student exam scores has two clear peaks — one near 65 and another near 90 — with a dip between them. This shape is called:

    1. A.Symmetric
    2. B.Right-skewed
    3. C.Bimodal
    4. D.Uniform

2.3 – 2.4 — Median, Quartiles, IQR, Five-Number Summary

  1. 4.

    Find the median of the data set 12, 8, 15, 22, 7, 19, 11.

    1. A.11
    2. B.12
    3. C.13.5
    4. D.14
  2. 5.

    The interquartile range (IQR) is computed as:

    1. A.Q₃ − Q₁
    2. B.Q₃ + Q₁
    3. C.Maximum − Minimum
    4. D.Mean − Median
  3. 6.

    The third quartile Q₃ is the same as the:

    1. A.25th percentile
    2. B.50th percentile (median)
    3. C.75th percentile
    4. D.100th percentile
  4. 7.

    The five-number summary consists of:

    1. A.Mean, median, mode, range, IQR
    2. B.Min, Q₁, Median, Q₃, Max
    3. C.Min, mean, median, mode, max
    4. D.Q₁, Q₂, Q₃, Q₄, Q₅

2.5 — Mean, Median, Mode, and Resistance

  1. 8.

    For the data set 14, 19, 19, 22, 25, 19, 30, 18, the mode is:

    1. A.18
    2. B.19
    3. C.20.75
    4. D.22
  2. 9.

    Which symbol represents the mean of a population?

    1. A.x̄
    2. B.μ
    3. C.s
    4. D.n
  3. 10.

    Which measure of center is most resistant to outliers?

    1. A.Mean
    2. B.Median
    3. C.Range
    4. D.Variance
  4. 11.

    A small data set has the values 100, 110, 120, 130, 200. If we replace the value 200 with 2,000, which statistic changes the most?

    1. A.Mode
    2. B.Median
    3. C.Mean
    4. D.Q₁

2.6 — Skewness

  1. 12.

    In a typical right-skewed (positively skewed) distribution:

    1. A.Mean < Median < Mode
    2. B.Mean ≈ Median ≈ Mode
    3. C.Mode < Median < Mean
    4. D.Median < Mean < Mode
  2. 13.

    A roughly bell-shaped, symmetric distribution has:

    1. A.A mean much greater than the median
    2. B.A mean approximately equal to the median
    3. C.A mean much less than the median
    4. D.No mode

2.7 — Range, Variance, and Standard Deviation

  1. 14.

    The range of a data set is computed as:

    1. A.Maximum − Minimum
    2. B.Q₃ − Q₁
    3. C.Mean − Standard deviation
    4. D.Mean + Standard deviation
  2. 15.

    The standard deviation is:

    1. A.The square of the variance
    2. B.The square root of the variance
    3. C.The mean of the absolute deviations
    4. D.The range divided by 4
  3. 16.

    If the sample variance is s² = 49, the sample standard deviation s is:

    1. A.7
    2. B.14
    3. C.24.5
    4. D.49
  4. 17.

    When computing the variance of a sample, we divide the sum of squared deviations by:

    1. A.n
    2. B.n − 1
    3. C.n + 1
    4. D.N

Z-Scores

  1. 18.

    A z-score of −1.5 means the data value is:

    1. A.1.5 standard deviations above the mean
    2. B.1.5 standard deviations below the mean
    3. C.1.5 units below the mean
    4. D.1.5% below the mean
  2. 19.

    On a national test with mean μ = 500 and standard deviation σ = 100, Carlos scored 620. His z-score is:

    1. A.0.62
    2. B.1.0
    3. C.1.2
    4. D.6.2
  3. 20.

    Maria gets a z-score of 1.8 on her math exam. Juan gets a z-score of 1.2 on his history exam. Who performed relatively better?

    1. A.Maria
    2. B.Juan
    3. C.They performed equally well
    4. D.Cannot be determined