Question

what was the median number of siblings?

Explanation:

Step1: Calculate the total number of students

Let's assume the frequencies for \(0\) siblings is \(a = 40\), for \(1\) sibling is \(b = 40\), for \(2\) siblings is \(c = 10\), for \(3\) siblings is \(d = 30\), for \(4\) siblings is \(e = 60\), for \(5\) siblings is \(f = 30\).
The total number of students \(n=a + b + c + d+e + f=40 + 40+10 + 30+60 + 30=210\)

Step2: Find the position of the median

Since \(n = 210\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=\frac{210}{2}=105\) and \(\frac{n}{2}+1 = 106\)

Step3: Cumulative frequency calculation

• Cumulative frequency for \(0\) siblings: \(CF_0=40\)
• Cumulative frequency for \(1\) siblings: \(CF_1=40 + 40=80\)
• Cumulative frequency for \(2\) siblings: \(CF_2=80+10 = 90\)
• Cumulative frequency for \(3\) siblings: \(CF_3=90 + 30=120\)

Since \(90\lt105\) and \(90\lt106\lt120\)

Answer:

\(3\)