Chapter 12: Information Handling

Solve · page 233: Example 13: The heights of 100 athletes, measured to the nearest (inches) are given in the following table. Find the median. Heignts | 62.5-63.5 |63.5-64.5 |64.5-65.5 |65.5-66.5 |66.5-67.5 |(67.5-68.5 168.5-69.5 | 69.5-70.5 Heigh |70.5-71.5 (in inches) Students

Solution $$n = \sum f = 100$$ $$\frac{n}{2} = \frac{100}{2} = 50$$ $$\text{Median} = l + \frac{h}{f} \left( \frac{n}{2} - c \right)$$ $$l = 66.5, \quad h = 1, \quad f = 30, \quad c = 40$$ $$\text{Median} = 66.5 + \frac{1}{30} (50 - 40)$$ $$\text{Median} = 66.5 + \frac{1}{30} (10)$$ $$\text{Median} = 66.5 + \frac{10}{30}$$ $$\text{Median} = 66.5 + 0.333$$ $$\mathbf{66.833 \text{ inches}}$$

Explanation

• Total frequency ($n$ [تعداد]) found by summing all individual frequencies.
• Half of the total frequency ($\frac{n}{2}$) calculated to locate the median group.
• Median formula (میڈین) stated with lower class boundary ($l$), class interval size ($h$), frequency ($f$), and cumulative frequency preceding the median class ($c$).
• Values for $l$, $h$, $f$, and $c$ identified from the median class in the frequency table.
• Values substituted into the median formula.
• Subtraction performed inside the parentheses.
• Multiplication performed between the fraction and the difference.
• Fraction simplified to a decimal value.
• Addition performed to find the final median height.