Question

10/23 unit 2 the normal distribution quiz review
in a perfectly normal distribution, which of the following is (are) true?
i. the mean and the median are equal.
ii. 50% of the data is below the mean.
iii. a data value 1.5 standard deviations below the mean is an outlier.
o i only
o i and ii only
o i and iii only
o i, ii, and iii

Explanation:

• For statement I: In a perfectly normal distribution, the distribution is symmetric. The mean, median, and mode all lie at the center of the distribution. So, the mean and the median are equal.
• For statement II: Since the normal distribution is symmetric about the mean, 50% of the data lies below the mean and 50% lies above the mean.
• For statement III: The outlier rule (1.5 - IQR rule) is for skewed distributions (e.g., box - plots). For a normal distribution, we use the empirical rule (68 - 95 - 99.7 rule). A data value 1.5 standard deviations below the mean is not an outlier in a normal distribution.

Answer:

I and II only