Question

Find the mean deviation from the mean of the given data :

• A. $10$
• B. $3$
• C. $3.319$
• D. $2.19$

Answer 1

Answer: (C)

$3.319$

$x^{i}46810121416$ $f^{i}2553214\_\_\_\_\_\_\_\_\_\_\_\_\_\sum f_i=22$ $Cumulativefrequency5+2=77+5=1212+3=1515+2=1717+1=1818+4=22$ $f_{i}x08304030241464\_\_\_\_\_\_\_\_\_200$

$|x_i-\overline{x}||4-\frac{100}{11}|=\frac{56}{11}|6-\frac{100}{11}|=\frac{66}{11}|8-\frac{100}{11}|=\frac{12}{11}|10-\frac{100}{11}|=\frac{10}{11}|12-\frac{100}{11}|=\frac{32}{11}|14-\frac{100}{11}|=\frac{54}{11}|16-\frac{100}{11}|=\frac{76}{11}$ $f_i\left|x_{i-}\overline{x}\right|\frac{112}{11}\frac{220}{11}\frac{60}{11}\frac{30}{11}\frac{64}{11}\frac{54}{11}\frac{304}{11}\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\sum f_i|x_i-\overline{x}|=\frac{844}{11}$

Therefore, $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{200}{22}=\frac{100}{11}$

Therefore, mean $\left(\overline{x}\right)$ $=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}=\frac{100}{11\ast 22}=\frac{50}{121}=3.31$.