Find the mean for the following data set?

Question

Values ${10, 15, 20, 25, 30}$ ${10,15,20,25,30}$
Frequency ${5, 10, 7, 8, 2}$ ${5,10,7,8,2}$

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Answer 1 · 2016-09-06T08:31:25

Mean is $18.75$ $18.75$

It is apparent that while $X_{i}$ $X_i$ have values ${10, 15, 20, 25, 30}$ ${10,15,20,25,30}$

and their respective $F_{i}$ $F_i$ are frequencies of their occurrence in that order i.e. ${5, 10, 7, 8, 2}$ ${5,10,7,8,2}$

Mean of such distribution is given by

$\frac{\sum (X_{i} \times F_{i})}{\sum F_{i}}$ $(sum(X_ixxF_i))/(sumF_i)$

= $\frac{10 \times 5 + 15 \times 10 + 20 \times 7 + 25 \times 8 + 30 \times 2}{5 + 10 + 7 + 8 + 2}$ $(10xx5+15xx10+20xx7+25xx8+30xx2)/(5+10+7+8+2)$

= $\frac{50 + 150 + 140 + 200 + 60}{32}$ $(50+150+140+200+60)/32$

= $\frac{600}{32} = 18.75$ $600/32=18.75$