The first quartile

The first quartile

a. contains at least one third of the data elements
b. is the same as the 25th percentile
c. is the same as the 50th percentile
d. is the same as the 75th percentile

The correct answer and explanation is :

The correct answer is b. is the same as the 25th percentile.

Explanation:

The first quartile (Q1) is a measure used in descriptive statistics to divide a data set into four equal parts. Quartiles are values that split the data set into four intervals, each containing approximately 25% of the data. These intervals help understand the distribution and spread of the data.

1. First Quartile (Q1):

• The first quartile is the value below which 25% of the data fall. In other words, it represents the 25th percentile of the data.
• To find the first quartile, you first organize the data in ascending order, then identify the data point that divides the lower 25% of the data from the rest.
• The first quartile is an important statistic because it helps identify the lower boundary of the central data, showing the spread of the lower portion of the dataset.

1. Explanation of Incorrect Answers:

• a. contains at least one third of the data elements: This is incorrect because the first quartile contains only 25% of the data, not one-third (approximately 33%).
• c. is the same as the 50th percentile: This is incorrect because the 50th percentile is actually the median, which divides the data set into two equal halves. The first quartile is the 25th percentile, and the second quartile (median) is the 50th percentile.
• d. is the same as the 75th percentile: This is incorrect because the 75th percentile is known as the third quartile (Q3), not the first. The third quartile is the value below which 75% of the data fall.

Summary:

The first quartile (Q1) corresponds to the 25th percentile, meaning it is the data point below which 25% of the values in the dataset fall. This is essential for understanding the distribution of the lower portion of a dataset and plays a key role in creating box plots and other statistical analyses.