Question

computer range, Percentile range and its coefficient÷ 55,60,70,70,90,110,120,130,145,145,155,170​

Answer 1

$\boxed{\begin{tabular}{ c || c } \bf{Size} & \bf{Frequency} \\ \cline{1-2}\sf{55} & \sf{1} \\ \cline{1-2}\sf{60} & \sf{1} \\ \cline{1-2}\sf{70} & \sf{2} \\ \cline{1-2}\sf{90} & \sf{1} \\ \cline{1-2}\sf{110} & \sf{1} \\ \cline{1-2}\sf{120} & \sf{1} \\ \cline{1-2}\sf{130} & \sf{1} \\ \cline{1-2}\sf{145} & \sf{2} \\ \cline{1-2}\sf{155} & \sf{1} \\ \cline{1-2}\sf{170} & {1} \\ \end{tabular}}$

Firstly let's find the Range of this discrete series :-

${\boxed{\sf{\implies Range \: = \: H - L }}}$

• H = Highest value in series .

• L = Lowest value in series.

$\sf{\implies 170 \: is \: H\: and\: 55 \; is\: L}$

$\sf{\implies 170-55 = 115}$

${\boxed{\sf{\implies 115\: is \: the\: Range. \: of \: given\: series}}}$

Now we'll find coefficient of range

${\boxed{\sf{\implies Coefficient \:of\:Range \: = \: \frac{H - L}{H+L} }}}$

$\sf{\implies \dfrac{170-55}{170+55}}$

$\sf{\implies \dfrac{115}{225} = 0. 52}$

${\boxed{\sf{\implies Coefficient\: of \: Range \: is\: 0.52}}}$

Now let's find Percentile.

${\boxed{\sf{\implies Percentile_{70} \: = \: 70 \times ( \dfrac{n +1 }{100}) th \: term }}}$

$\sf{\implies P_{70} = 70\times ( \dfrac{ 12+1}{100}) }$

$\sf{\implies P_{70} = 70 \times 0.13 \: = \: 9.1 \: th \: term }$

9.1 firstly appear in C. F of 10th term of given series and size corresponding to it is 145 .

${\boxed{\sf{\implies P_{70} \: is \: 145}}}$