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One-Variable Data: Distributions and Measures of Center and Spread Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 One-Variable Data: Distributions and Measures of Center and Spread flashcards as text

  1. Which of the following correctly describes a right-skewed (positively skewed) distribution?

    Answer: The tail extends to the right and the mean is greater than the median.

    In a right-skewed distribution, the longer tail is on the right, which pulls the mean above the median.

  2. A data set has 7 values with a median of 18. A new value of 5 is added to the dataset, making it 8 values total. What is the new median?

    Answer: It cannot be determined without knowing all values.

    Without knowing the specific values around the median, we cannot calculate the exact new median; we only know the original median was 18 and a smaller value was added.

  3. The standard deviation of a dataset is 0. Which of the following must be true?

    Answer: All values in the dataset are equal.

    A standard deviation of 0 means there is no variation; every value in the dataset must be identical to the mean.

  4. A dataset of 6 values: 4, 9, 11, x, 18, 22 is sorted in ascending order and has a median of 13. What is the value of x?

    Answer: 15

    With 6 values, the median is the average of the 3rd and 4th values: (11 + x) ÷ 2 = 13, so 11 + x = 26, giving x = 15.

  5. A dataset has values 6, 9, 12, 15, 18. If each value is decreased by 3, which of the following changes?

    Answer: The mean

    Subtracting a constant from every value shifts the mean down by that constant but does not change the range or standard deviation, since those measure spread.

  6. In a box plot, approximately what percent of the data lies between Q1 and Q3?

    Answer: 50%

    By definition, Q1 marks the 25th percentile and Q3 marks the 75th percentile, so the interquartile range (IQR) contains the middle 50% of the data.

  7. The heights (in inches) of 5 basketball players are 72, 75, 76, 78, and 79. If a 6th player with a height of 84 inches joins, which measure of center increases the most?

    Answer: Mean

    The mean is sensitive to extreme values; adding 84, which is much larger than the current mean of 76, increases the mean more than it shifts the median.