Question

compare the values and calculate the median of the given data.

Explanation:

Step1: Count the total number of data points

Count all the dots in the dot - plot. There are \(2 + 7+4 + 4+2+1=20\) data points.

Step2: Find the position of the median

Since \(n = 20\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=\frac{20}{2} = 10\) and \(\frac{n}{2}+1=11\).

Step3: Cumulative frequency

Start from the lowest value:

• For \(x = 0\), cumulative frequency \(cf_0=2\)
• For \(x = 1\), cumulative frequency \(cf_1=2 + 7=9\)
• For \(x = 2\), cumulative frequency \(cf_2=9+4 = 13\)

The 10th and 11th values fall in the \(x = 2\) category.

Answer:

The median of the data is \(2\)