From the data given below,state which group is more variable,$A$ or $B$?
Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ Group $A$ $9$ $17$ $32$ $33$ $40$ $10$ $9$ Group $B$ $10$ $20$ $30$ $25$ $43$ $15$ $7$
| Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
| Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
| Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
(B) To determine which group is more variable,we compare their standard deviations. Since the means of both groups are equal,the group with the higher standard deviation is more variable.
For Group $A$:
Mean $\bar{x}_A = 44.6$,Variance $\sigma_A^2 = 227.84$,Standard Deviation $\sigma_A = \sqrt{227.84} \approx 15.09$.
For Group $B$:
Mean $\bar{x}_B = 44.6$,Variance $\sigma_B^2 = 243.84$,Standard Deviation $\sigma_B = \sqrt{243.84} \approx 15.61$.
Since $\sigma_B > \sigma_A$,Group $B$ is more variable.
For Group $A$:
Mean $\bar{x}_A = 44.6$,Variance $\sigma_A^2 = 227.84$,Standard Deviation $\sigma_A = \sqrt{227.84} \approx 15.09$.
For Group $B$:
Mean $\bar{x}_B = 44.6$,Variance $\sigma_B^2 = 243.84$,Standard Deviation $\sigma_B = \sqrt{243.84} \approx 15.61$.
Since $\sigma_B > \sigma_A$,Group $B$ is more variable.
Explore More
Similar Questions
The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each,$10$ items gave an outcome $\frac{1}{2}$ each,and the remaining $10$ items gave an outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$,then $|d|$ equals:
DifficultJEE MAIN 2019
View SolutionThe coefficient of variation and standard deviation of an ungrouped data are $60$ and $21$ respectively. If $15$ is added to every observation of the data,then the coefficient of variation of the new data is
In an experiment with $15$ observations for $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:
Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?
Two dice $A$ and $B$ are rolled. Let the numbers obtained on $A$ and $B$ be $\alpha$ and $\beta$ respectively. If the variance of $\alpha - \beta$ is $\frac{p}{q}$,where $p$ and $q$ are coprime,then the sum of the positive divisors of $p$ is equal to
DifficultJEE MAIN 2023
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo