Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests. Ravi 25 Hashina 10 Who is more intelligent and who is more consistent?

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests.
\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|} \hline \text { Ravi } & 25 & 50 & 45 & 30 & 70 & 42 & 36 & 48 & 35 & 60 \\ \hline \text { Hashina } & 10 & 70 & 50 & 20 & 95 & 55 & 42 & 60 & 48 & 80 \\ \hline \end{array}
Who is more intelligent and who is more consistent?

Answers (1)

The marks obtained, out of 100, by 2 students Ravi and Hashina in 10 tests are given  

  We have to find who is  more intelligent and who is more consistent

  The marks of Ravi taken separately as follows

\begin{array}{|l|l|l|} \hline \multicolumn{1}{|c|} {x_{i}} & \multicolumn{1}{|c|} {d_{i}=x_{i}-45} & \multicolumn{1}{|c|} {d_{i}^{2}} \\ \hline 25 & -20 & 400 \\ \hline 50 & 5 & 25 \\ \hline 45 & 0 & 0 \\ \hline 30 & -15 & 225 \\ \hline 70 & 25 & 625 \\ \hline 42 & -3 & 9 \\ \hline 36 & -9 & 81 \\ \hline 48 & 3 & 9 \\ \hline 35 & -10 & 100 \\ \hline 60 & 15 & 225 \\ \hline \text { TOTAL }=441 & =-9 & =1699 \\ \hline \end{array}

Here we have assumed 45 as mean

And we know that the standard deviation can be written as, 

\\ \sigma =\sqrt {\frac{ \Sigma \left( x-a \right) ^{2}}{n}- \left( \frac{ \Sigma \left( x-a \right) }{n} \right) ^{2}}~~ \\\\ \\ \sigma =\sqrt {\frac{1699}{10}- \left( -\frac{9}{10} \right) ^{2}} =\sqrt {169.9-0.81}= \sqrt {169.09}~=13 \\\\ \\ \text{Now mean is }\overline{x}=A+\frac{ \Sigma f_{i}d_{i}}{N}~ =45- \left( \frac{9}{10} \right) =44.1~~ \\\\ \\ \text{ For Hashina} \\\\

\begin{array}{|l|l|l|} \hline \multicolumn{1}{|c|} {x_{i}} & \multicolumn{1}{|c|} {d_{i}=x_{i}-53} & \multicolumn{1}{|c|} {d_{i}^{2}} \\ \hline 10 & -43 & 1849 \\ \hline 70 & 17 & 289 \\ \hline 50 & -3 & 9 \\ \hline 20 & -33 & 1089 \\ \hline 95 & 42 & 1764 \\ \hline 55 & 2 & 4 \\ \hline 42 & -11 & 121 \\ \hline 60 & 7 & 49 \\ \hline 48 & -5 & 25 \\ \hline 80 & 27 & 729 \\ \hline \text { TOTAL }=530 & =0 & =5928 \\ \hline \end{array}

Here as  \\\\ \frac{530}{10}=53~~So, 53 is mean \\\\


 And we know that the standard deviation can be written as, 

\sigma =\sqrt {\frac{ \Sigma \left( x-a \right) ^{2}}{n}- \left( \frac{ \Sigma \left( x-a \right) }{n} \right) ^{2}}~~ \\\\ \\ \sigma =\sqrt {\frac{5928}{10}- \left( -\frac{0}{10} \right) ^{2}} =\sqrt {592.8}=24.35 \\\\ \\ \text{ We have the mean and S.D of the Hashina and Ravi . } \\\\ \\ \text{For Ravi , C.V}=\frac{ \sigma }{\overline{x~}} * 100=\frac{13}{44.1} * 100 =29.48 \\\\
 \\ For Hasina , C.V=\frac{ \sigma }{\overline{x~}} * 100=\frac{24.35}{53} * 100~=45.94~ \\\\ \\ \text{ Now as CV } \left( \text{of Ravi } \right) <\text{CV of Hasina} \\\\ \\ \text{~Hence, Ravi is more consistent } \\\\ \\ \text{ Mean of Hasina}>\text{Mean of Ravi } \\\\ \\ \text{~ Hence, Hasina is more intelligent} \\\\

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question