To compare two histograms fairly, both should use

Answer: Same axis scales (and bin widths) Common scales prevent visual misinterpretation when comparing distributions.

Which statement about A and B is correct?

Answer: A's mean A's median; B's mean < B's median Right-skew: mean pulled right of median. Left-skew: mean pulled left of median.

Comparing the two distributions, which has a smaller standard deviation?

Answer: B (more concentrated near center) Distribution B has more mass piled at the center with thinner tails, indicating less spread and a smaller SD.

AP Statistics · Topic 1.9

Comparing Distributions of a Quantitative Variable Practice

Q: Comparing the two distributions, which has a smaller standard deviation?

Answer: B (more concentrated near center) Distribution B has more mass piled at the center with thinner tails, indicating less spread and a smaller SD.

Part of Exploring One-Variable Data.(UNC-1.G)

Practice questions

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Sample questions

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Sample 1difficulty 3/5
$To compare two histograms fairly, both should use$
- A
  $Different bin counts$
- B
  $Different scales$
- C
  $Different x-axes$
- D
  $Same axis scales (and bin widths)$
  check_circle
Why
$Common scales prevent visual misinterpretation when comparing distributions.$
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Sample 2difficulty 3/5
$Two histograms show different distribution shapes.$
$Which statement about A and B is correct?$
- A
  $Both means equal both medians$
- B
  $A's mean < A's median; B's mean > B's median$
- C
  $Cannot determine without numbers$
- D
  $A's mean > A's median; B's mean < B's median$
  check_circle
Why
$Right-skew: mean pulled right of median. Left-skew: mean pulled left of median.$
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Sample 3difficulty 3/5
$Histograms A and B both have the same mean.$
$Comparing the two distributions, which has a smaller standard deviation?$
- A
  $A (more concentrated near center)$
- B
  $B (more concentrated near center)$
  check_circle
- C
  $Cannot tell$
- D
  $Both have equal SD$
Why
$Distribution B has more mass piled at the center with thinner tails, indicating less spread and a smaller SD.$
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Sample 4difficulty 3/5
$Boxplots show salaries for male (M) and female (F) employees at one company.$
$Which comparison is best supported?$
- A
  $Females have higher maximum$
- B
  $Both have identical centers$
- C
  $Males' median salary is higher than females'$
  check_circle
- D
  $Males earn less on average$
Why
$The median line of M is to the right (higher) than the median line of F, indicating higher central salary for males.$
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Sample 5difficulty 3/5
$From the side-by-side boxplots, the typical (median) value is larger for$
- A
  $Group A (lower box)$
  check_circle
- B
  $Same$
- C
  $Cannot tell$
- D
  $Group B$
Why
$Group A's median line is at a smaller y (higher value if y-axis is value); choose by where the median sits.$
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