Question

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Explanation:

Analyze the shape of the histogram

The histogram displays the distribution of ponytail lengths. We observe the heights of the bars for each interval from left to right:

• \(10\text{--}10.9\): 1
• \(11\text{--}11.9\): 4
• \(12\text{--}12.9\): 5
• \(13\text{--}13.9\): 4
• \(14\text{--}14.9\): 2
• \(15\text{--}15.9\): 4

Evaluate skewness and symmetry

• A distribution is skewed left if it has a long tail on the left side.
• A distribution is skewed right if it has a long tail on the right side.
• A distribution is symmetrical if the left and right sides are approximately mirror images.
• Looking at the data, there is a tail extending to the left (the single low value in the \(10\text{--}10.9\) range), and the peak is around \(12\text{--}12.9\). However, the right side also rises back up to 4 at the \(15\text{--}15.9\) interval, making it asymmetric and irregular.
• Let's re-examine standard definitions for school curricula: a distribution with a longer tail on the left is classified as "skewed left". Here, the lower values stretch out further to the left (down to 10) with a very low frequency (1), whereas the right side ends abruptly at 15.9 with a high frequency (4). This creates a longer tail on the left side, indicating a left-skewed distribution.

Match with the options

• A. skewed left
• B. skewed right
• C. no visible pattern
• D. symmetrical and balanced

The presence of the left tail makes "skewed left" the most appropriate classification.

Answer:

• (A) skewed left (Correct answer)
• (B) skewed right
• (C) no visible pattern
• (D) symmetrical and balanced