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 use the formula \(n=\sum f\).

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

Step2: Cumulative frequency

Score,\(x\)	Frequency,\(f\)	Cumulative Frequency
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 \(10^{th}\) and \(11^{th}\) data items fall in the score \(x = 4\) (because cumulative frequency up to \(x = 3\) is \(9\) and cumulative frequency up to \(x=4\) is \(14\)).

Step3: Calculate the median

Since both the \(10^{th}\) and \(11^{th}\) data items are \(4\), the median \(M=\frac{4 + 4}{2}=4\)

Answer:

\(4\)