Question

find the median for the data items in the frequency distribution.
the median is

Explanation:

Step1: Calculate the total number of data items

We sum up the frequencies: \(n = 5+1 + 3+5+3+1+1+1=20\)

Step2: Determine the position of the median

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

Step3: Calculate the cumulative frequencies

Score \(x\)	Frequency \(f\)	Cumulative Frequency \(cf\)
2	1	5 + 1=6
3	3	6+3 = 9
4	5	9 + 5=14
5	3	14+3=17
6	1	17 + 1=18
7	1	18+1=19
8	1	19+1=20

The 10th and 11th data values fall in the score \(x = 4\) category (because \(cf\) for \(x = 3\) is \(9\) and \(cf\) for \(x = 4\) is \(14\))

Answer:

\(4\)