DAV Class 7 Maths Chapter 12 Enrichment Question

DAV Class 7 Maths Chapter 12 Enrichment Question

Data Handling Enrichment Question


1. Find the mean, median and mode of the following observations.

\( \displaystyle 75\%, 3.2 , 450\%, 0.25, 3\frac{1}{5},1.54 \)

Solution

\begin{align*} & 75\%, 3.2 , 450\%, 0.25, 3\frac{1}{5},1.54 \\ \\ 75\% &= \frac{75}{100} \implies 0.75 \\ \\ 450\% &= \frac{450}{100} \implies 4.5 \\\\ 3\frac{1}{5} &= \frac{16}{5} \implies 3.2 \\ \\\color{orange}Observations & = 0.75, 3.2 , 4.5, 0.25, 3.2,1.54 \\ \\& \color{magenta} \boxed{Mean} \\ \text{Mean} &= \frac{\text{Sum of all observations}}{\text{No. of observations}} \\ \\ &= \frac{0.25 + 0.75 + 1.54 + 3.2 + 3.2 + 4.5}{6} \\ &= \frac{13.44}{6} \\ \\ \color{green} Mean &=\color{green} 2.24 \\ \\ & \color{magenta} \boxed{Median} \\ \text{Ascending order} & = \cancel{0.25}, \cancel{ 0.75}, 1.54, 3.2, \cancel{3.2}, \cancel{4.5} \\ \\ \text{Median} &= \frac{\text{Sum of two middle most observations}}{2} \\ \\ &= \frac{1.54 + 3.2}{2} \\ \\ &= \frac{4.74}{2} \\ \\ \color{green} Median &= \color{green} 2.37 \\ \\& \color{magenta} \boxed{Mode} \\ \text{Mode} &= \text{The most frequently occurring value} \\ \text{Ascending order} & = 0.25, 0.75, 1.54, {\color{magenta}3.2, 3.2}, 4.5 \\ &= 3.2 \quad \text{(appears 2 times)} \\ \color{green} Mode &= \color{green} 3.2 \\ \\ \end{align*}

Answer Mean \( = \color{red} 2.24 \) , Median \( = \color{red} 2.37 \), Mode \( = \color{red} 3.2 \)