Question

self-check
given the histogram above, find the median.

Explanation:

Step1: Find the total number of data points

From the histogram, the frequencies are \(2\) (for \(x = 0\)), \(7\) (for \(x = 1\)), \(4\) (for \(x = 2\)), \(2\) (for \(x = 3\)), \(1\) (for \(x = 4\)). The total number of data points \(n=2 + 7+4 + 2+1=16\)

Step2: Determine the position of the median

Since \(n = 16\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=\frac{16}{2} = 8\) and \(\frac{n}{2}+1=9\)

Step3: Cumulative frequency

For \(x = 0\), cumulative frequency \(CF_0=2\)
For \(x = 1\), cumulative frequency \(CF_1=2 + 7=9\)

Since the \(8\)th and \(9\)th values fall in the \(x = 1\) class (because \(CF_0=2<8\) and \(CF_1 = 9\geq8\))

Answer:

\(1\)