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 \(n=\sum f\).

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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 ordered data values. \(\frac{n}{2}=\frac{20}{2}=10\) 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 values fall in the \(x = 4\) category (because \(cf\) for \(x = 3\) is 9, and \(cf\) for \(x=4\) is 14).

Answer:

4