Descriptive statistics: one variable

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. Area codes such as 770 are numbers. Is the area code of a phone number a quantitative variable?
    1. No: it is categorical, a label that only looks like a number
    2. Yes: its values are numbers
    3. Yes, a discrete quantitative variable
  2. A study measures the resting heart rate of 29 runners. What are the cases (observational units)?
    1. The 29 runners
    2. The heart rates
    3. The number 29
  3. A distribution of incomes has mean 54 thousand dollars and median 43 thousand dollars. What is its most likely shape?
    1. Skewed right: a long tail of high values pulls the mean up
    2. Skewed left
    3. Symmetric
  4. 43 students name their favorite sport. Which display suits these data?
    1. A bar chart
    2. A histogram
    3. A boxplot
  5. Which four features should you describe for the distribution of a quantitative variable (here, 42 test scores)?
    1. Shape, center, spread and unusual values (outliers)
    2. The mean, the median, the mode and the sample size
    3. The type of graph, the title, the axes and the colors
  6. Find the mean of the data 5, 11, 24, 33, 41.
  7. Find the median of the data 9, 14, 24, 37, 44, 79.
  8. One value in a data set is changed from 20 to 712. What happens to the mean and the median?
    1. The mean increases; the median stays about the same
    2. Both increase by the same amount
    3. The median increases; the mean stays the same
  9. Find the interquartile range (IQR) of the 8 values 3, 9, 14, 17, 24, 27, 33, 46.
  10. Find the (sample) standard deviation of 33, 38, 43.
  11. Two classes both have mean score 78. In class A the scores range from 76 to 80; in class B from 63 to 93. Which has the larger standard deviation?
    1. Class B: its scores are more spread out
    2. Class A
    3. The same, because the means are equal
  12. A data set has Q1=24Q_1 = 24 and Q3=32Q_3 = 32. Above which value is a data point an outlier by the 1.5×IQR1.5 \times \text{IQR} rule?