Question

give the names of two other statistics that have the same value as the 50th percentile.

choose the correct answer below.

a. first quartile; midrange
b. second quartile; median
c. second quartile; mean
d. third quartile; mode

Explanation:

Identify the 50th percentile

The 50th percentile is the value below which 50% of the data points in a distribution fall.

Relate to other statistical measures

• The median is the middle value of a data set, splitting it into two equal halves (50% below and 50% above). Thus, the median is equal to the 50th percentile.
• Quartiles divide a data set into four equal parts. The second quartile (\(Q_2\)) represents the 50% mark of the data, which is identical to both the median and the 50th percentile.

Evaluate the given options

• Option A: First quartile (\(Q_1\), 25th percentile) and midrange are not equal to the 50th percentile.
• Option B: Second quartile and median are both equal to the 50th percentile.
• Option C: Second quartile is equal, but the mean is generally different unless the distribution is perfectly symmetric.
• Option D: Third quartile (\(Q_3\), 75th percentile) and mode are not equal to the 50th percentile.

Answer:

• (A) First quartile; midrange
• (B) Second quartile; median (Correct answer)
• (C) Second quartile; mean
• (D) Third quartile; mode