The mean of the following frequency is 50 0-20 1720-40 f140-60 3260-80

1.	The mean of the following frequency is 50 0-20 1720-40 f140-60 3260-80 f280-100 19
Answer»		\t\t\t0-20 20-40 40-60 60-80 80-10017 p 32 24 1910 30 50 70 90170 30p 1600 1680 1710Total{tex}\\sum {{f_i}} = p + 92{/tex}\xa0{tex}\\sum {{f_i}} {x_i} = 30p + 5160{/tex}\tUsing the direct method,{tex}\\overline x = \\frac{{\\sum {{f_i}{x_i}} }}{{\\sum {{f_i}} }}{/tex}{tex} \\Rightarrow 50 = \\frac{{30p + 5160}}{{p + 92}}{/tex}\xa0{tex} \\Rightarrow {/tex}\xa030p + 5160 = 50 (p + 92){tex} \\Rightarrow {/tex}\xa030p + 5160 = 50p + 4600\xa0{tex} \\Rightarrow {/tex}\xa050p - 30p = 5160 - 4600{tex} \\Rightarrow {/tex}\xa020p = 560{tex} \\Rightarrow p = \\frac{{560}}{{20}} {/tex}{tex}\\Rightarrow p = 28{/tex}Hence, the value of p is 28.

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