Question

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

Explanation:

Step1: Calculate the total number of data items

The total number of data items \( n=\sum f\).
\(n = 5+1+3+5+3+1+1+1=20\)

Step2: Determine 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 ordered data items. \(\frac{n}{2}=\frac{20}{2} = 10\) and \(\frac{n}{2}+1=11\)

Step3: Cumulative frequency

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 items fall in the \(x = 4\) group (because \(cf\) for \(x = 3\) is 9 and \(cf\) for \(x=4\) is 14)

Answer:

\(4\)