Question

find the median for the data items in the given frequency distribution

the median is
(type an integer or a decimal)

Explanation:

Step1: Calculate the total number of data items

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

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Step2: Find the position of the median

Since \(n = 30\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th data items. \(\frac{n}{2}=\frac{30}{2} = 15\) and \(\frac{n}{2}+1=16\)

Step3: Cumulative frequency calculation

Score (\(x\))	Frequency (\(f\))	Cumulative Frequency (\(cf\))
2	3	3 + 3=6
3	4	6+4 = 10
4	3	10+3=13
5	6	13 + 6=19
6	2	19+2=21
7	3	21+3=24
8	6	24+6=30

The 15th and 16th data items fall within the score \(x = 5\) (because \(cf\) for \(x = 4\) is 13 and \(cf\) for \(x=5\) is 19)

Answer:

\(5\)