Question

A data set has 40 data points. Enter values to answer each of the questions below. 1. How many points are above the median? 2. How many points are below the first quartile? 3. How many points are in between the first and third quartiles, aka the IQR? (Interquartile range)

Answer 1

1. Above the median: 20 data points.

2. Below the first quartile: 10 data points.

3. In the interquartile range (IQR): 20 data points.

Step-by-step explanation:

The median is the middle value in a dataset when arranged in ascending order. In a dataset with 40 data points, the median would be the average of the 20th and 21st values. Therefore, half of the data points, or 20, are above the median.

The first quartile (Q1) is the median of the lower half of the dataset. Since the dataset has 40 points, the lower half would be the first 20 points. So, 10 data points are below the first quartile.

The interquartile range (IQR) is the range between the first and third quartiles. With 40 data points, the IQR spans from the 10th to the 30th data point, including both. Thus, there are 20 data points in the interquartile range. The IQR is a measure of statistical dispersion and provides insights into the spread of the middle 50% of the data.