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 \(n = 24\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data items. \(\frac{n}{2}=\frac{24}{2}=12\), \(\frac{n}{2}+1 = 13\).

Step3: Cumulative frequency

Score \(x\)	Frequency \(f\)	Cumulative Frequency \(cf\)
2	5	2 + 5=7
3	4	7+4 = 11
4	2	11+2=13

The 12th and 13th data items fall in the score \(x = 3\) (because cumulative frequency up to \(x = 3\) is 11 and up to \(x=4\) is 13).

Answer:

\(3\)