The 50th percentile is the
a. mode
b. median
c. mean
d. third quartile
The correct answer and explanation is :
The correct answer is b. median.
Explanation:
In statistics, percentiles are used to understand and interpret the distribution of a set of data. The 50th percentile specifically refers to the value below which 50% of the data falls. This is known as the median.
Here’s why the 50th percentile is the median:
- Percentiles divide a data set into 100 equal parts. The n-th percentile represents the value below which n% of the data points fall.
- The 50th percentile is the value at the exact midpoint of the data set, meaning 50% of the values are below it, and 50% are above it.
- This is the definition of the median, which is the middle value in an ordered list of numbers. If there is an odd number of data points, the median is the middle value. If there is an even number of data points, the median is the average of the two middle values.
Clarifying the Other Choices:
- a. Mode: The mode refers to the most frequently occurring value(s) in a data set. It is not related to the position of values like percentiles or the median. For example, in the data set {2, 4, 4, 6}, the mode is 4 because it appears most frequently.
- c. Mean: The mean is the average of all the data points in a set. It is calculated by adding all the values and dividing by the number of values. While it provides a measure of central tendency, it does not specifically relate to percentiles, as it is not positioned at a specific point in the data distribution.
- d. Third Quartile: The third quartile (Q3) refers to the 75th percentile. It is the value below which 75% of the data points fall, and it represents a different measure of the data’s spread, not the 50th percentile.
Thus, the 50th percentile is the median, a key measure of central tendency.