Question

a data set has 40 data points. enter values to answer each of the questions below. how many data points are above the median? how many data points are below the 1st quartile? how many data points are between the 1st and the 3rd quartiles, or in the interquartile range (iqr)?

Explanation:

Step1: Recall the properties of median

The median divides the data set into two equal - halves. If there are \(n = 40\) data points, the number of data points above the median is \(\frac{n}{2}\).

$$ \frac{40}{2}=20 $$

Step2: Recall the properties of the first quartile

The first quartile (\(Q_1\)) divides the lower \(25\%\) of the data. The number of data points below \(Q_1\) is \(0.25n\).

$$ 0.25\times40 = 10 $$

Step3: Recall the properties of the inter - quartile range

The inter - quartile range (\(IQR=Q_3 - Q_1\)) contains \(50\%\) of the data. The number of data points in the \(IQR\) is \(0.5n\).

$$ 0.5\times40=20 $$

Answer:

1. \(20\)
2. \(10\)
3. \(20\)