Question

Answer of 1st and 2nd with steps

1. To draw a histogram to represent the following frequency distribution :

Class Interval	5-10	10-15	15-25	25-45	45-75
Frequency	6	12	10	8	15

the adjusted frequency for the class 25-45 is:

a) 6 b) 5 c) 3 d) 2

2. If the mean of the observations:
x, x+3, x+5, x+7, x+10
is 9, the mean of the last three observations is

a) $10\frac{1}{3}$ b) $10\frac{2}{3}$ c) $11\frac{1}{3}$ d) $11\frac{2}{3}$

Answer 1

Dear student
$$\begin{gathered} \mathrm{Mean}\mathrm{of}\mathrm{observations}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}} \\ \mathrm{Now},\mathrm{the}\mathrm{given}\mathrm{observations}\mathrm{are}: \\ \mathrm{x},\mathrm{x}+3,\mathrm{x}+5,\mathrm{x}+7,\mathrm{x}+10 \\ \mathrm{Now},\mathrm{mean}=\frac{\mathrm{x}+\mathrm{x}+3+\mathrm{x}+5+\mathrm{x}+7+\mathrm{x}+10}{5} \\ \Rightarrow 9=\frac{5\mathrm{x}+25}{5} \\ \Rightarrow 5\mathrm{x}+25=45 \\ \Rightarrow 5\mathrm{x}=20 \\ \Rightarrow \mathrm{x}=4 \\ \mathrm{So},\mathrm{the}\mathrm{observations}\mathrm{are}: \\ 4,7,9,11,14 \\ \mathrm{Now},\mathrm{the}\mathrm{maen}\mathrm{of}\mathrm{last}\mathrm{threre}\mathrm{observations}\mathrm{is} \\ \mathrm{Mean}=\frac{9+11+14}{3} \\ \Rightarrow \mathrm{x}=\frac{34}{3} \\ \Rightarrow \mathrm{x}=11\frac{1}{3} \end{gathered}$$
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