Question

find the mean and median for the following data 0-10,10-20,20-30,30-40,40-50, frequency is 8, 16, 36,34, 6

Answer 1

Answer:

0.09099999990&₹@-!)/₹37(?+_#36+(

Answer 2

Solution :

For mean drawn data :

$\begin{tabular}{|c|c|c|c|} \cline{1-4} \multicolumn{4} {|c|}{DATA} \\ \cline{1-4} \bf Class-Interval & \bf Frequency, (f_i) & \bf Class-mark, (x_i) & \bf f_i \bf x_i \\ \cline{1-4} 0-10 & 8 & 5 & 40 \\ \cline{1-4} 10-20 & 16 & 15 & 240 \\ \cline{1-4} 20-30 & 36 & 25 & 900 \\ \cline{1-4} 30-40 & 34 & 35 & 1190 \\ \cline{1-4} 40-50 & 6 & 45 & 270 \\ \cline{1-4} \bf Total & \sf \sum \sf f_i=100 & & \sum \sf f_i \sf x_i = 2640\\ \cline{1-4} \end{tabular}}$

$\underline{\bf{Explanation\::}}}$

Using formula of the mean :

$\boxed{\bf{Mean\:\bar x = \frac{\sum_ i f_i x_i }{\sum_ i f_i} }}}$

A/q

$\longrightarrow\sf{Mean\:( \bar x)=\cancel{\dfrac{2640}{100}} }\\\\\\\longrightarrow\bf{Mean\:(\bar x) = 26.4}$

∴ The mean will be 26.4 .

For median drawn data :

$\begin{tabular}{|c|c|c|} \cline{1-3} \multicolumn{3} {|c|} {DATA} \\ \cline{1-3} \bf Class-Interval & \bf Frequency, (f_i) & \bf Cumulative-frequency, (CF) \\ \cline{1-3} 0-10 & 8 & 8 \\ \cline{1-3} 10-20 & 16 & 24 \\ \cline{1-3} 20-30 & 36 & 60 \\ \cline{1-3} 30-40 & 34 & 94 \\ \cline{1-3} 40-50 & 6 & 100 \\ \cline{1-3} \bf Total & \sf N= \sf \sum \sf f_i = 100 & \\ \cline{1-3} \end{tabular}}$

$\underline{\bf{Explanation\::}}}$

Using formula of the median :

$\boxed{\bf{Median = l+\bigg(\dfrac{\frac{N}{2} -CF}{f}\bigg) \times h}}}}$

Where as;

• l is the lower limit of median class = 20
• N is the number of observations = 100
• CF is the cumulative frequency = 24
• h is the height of class = 10
• f is the frequency of median = 36

A/q

$\longrightarrow\sf{Median = 20 + \Bigg(\dfrac{\cancel{\dfrac{100}{2}} -24 }{36} \Bigg) \times 10}\\\\\\\longrightarrow\sf{Median = 20 + \bigg(\dfrac{50-24}{36} \bigg)\times 10}\\\\\\\longrightarrow\sf{Median = 20 + \dfrac{26}{36} \times 10}\\\\\\\longrightarrow\sf{Median = 20 + \cancel{\dfrac{260}{36} }}\\\\\\\longrightarrow\sf{Median = 20 + 7.22}\\\\\\\longrightarrow\bf{Median = 27.2}$

Thus;

The median will be 27.2 .