One-Variable Data: Distributions and Measures of Center and Spread Flashcards
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Read the first 7 One-Variable Data: Distributions and Measures of Center and Spread flashcards as text
The mean of five numbers is 14. Four of the numbers are 10, 12, 16, and 18. What is the fifth number?
Answer: 14
The total sum must be 14 × 5 = 70; the known four sum to 56, so the fifth number is 70 − 56 = 14.
A dot plot shows values: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the median?
Answer: 3
With 9 values, the median is the 5th value when sorted, which is 3.
A company reports employee salaries. The CEO earns $500,000 while most employees earn around $50,000. Which measure of center should HR use to most accurately represent the typical employee salary?
Answer: Median
The CEO's high salary would skew the mean upward, so the median better represents the typical employee salary.
Dataset A: {1, 5, 5, 5, 9} and Dataset B: {3, 4, 5, 6, 7}. Which dataset has the greater standard deviation?
Answer: Dataset A
Both datasets have a mean of 5, but Dataset A's values (1 and 9) are farther from the mean than Dataset B's extremes (3 and 7), giving Dataset A a larger standard deviation.
A box plot's median line is positioned closer to Q3 than to Q1. This suggests the distribution is:
Answer: Left-skewed
When the median is closer to Q3, the lower half of the data is more spread out, indicating a left-skewed distribution.
A dataset has mean 20 and standard deviation 4. A new dataset is created by doubling each value and subtracting 5. What is the new standard deviation?
Answer: 8
Subtracting 5 (a constant) doesn't affect standard deviation, but multiplying by 2 doubles it: 2 × 4 = 8.
The scores on a math quiz are: 55, 60, 65, 70, 75, 80, 85. If the lowest score (55) is removed, which of the following is true?
Answer: Both mean and median increase
Removing the lowest value (55) increases the mean because it was below the mean; the median also shifts from 70 to 72.5 with 6 values remaining.