Download App

LINEAR CORRELATION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsLINEAR CORRELATION4 Marks
Question
An educationalist has conducted an experiment to know the relation between the usage of Social Media in mobile phone and the result of the examination. A group of $10$ students is selected for this and the following results were obtained regarding, the time spent $x ($in hours$)$ in last week on Social Media and the marks $(2)$ obtained out of $50$ in the examination, taken immediately after it.
$\Sigma x=133, \Sigma y=220, \Sigma x^{2}=2344, \Sigma y^{2}=6500$ and $\Sigma x y=3500$
Later on, it was found that one of the pairs of observations of $X$ and $Y$ was taken as $(13, 20)$ instead of $(15, 25) .$
Find the correct value of the correlation coefficient between $X$ and $Y.$
✓

Answer

Here, $n=10, \Sigma x=133, \Sigma y=220, \Sigma x^{2}=2344, \Sigma y^{2}=6500$ and $\Sigma x y=3500$
Incorrect Pair $: (l 3, 20)$ Correct Pair $: (15,25)$
Now, we find corrected values of these measures as follows :
$\Sigma x=133-13+15=135$
$\Sigma y=220-20+25=225$
$\Sigma x^{2}=2344-(13)^{2}+(15)^{2}=2344-169+225=2400$
$\Sigma y^{2}=6500-(20)^{2}+(25)^{2}=6500-400+625=6725$
$\Sigma x y=3500-(13 \times 20)+(15 \times 25)=3500-260+375=3615$
Substituting these corrected values in the following formula,
$ r =\frac{n \Sigma x y-(\Sigma x)(\Sigma y)}{\sqrt{n \Sigma x^{2}-(\Sigma x)^{2}} \cdot \sqrt{n \Sigma y^{2}-(\Sigma y)^{2}}}$
$ =\frac{10(3615)-(135)(225)}{\sqrt{10(2400)-(135)^{2}} \cdot \sqrt{10(6725)-(225)^{2}}} $
$ =\frac{36150-30375}{\sqrt{24000-18225} \cdot \sqrt{67250-50625}}$
$ =\frac{5775}{\sqrt{5775} \cdot \sqrt{16625}}$
$ =\frac{5775}{\sqrt{96009375}}$
$ =\frac{5775}{9798.4374}$
$ =0.5894$
$\therefore r \simeq 0.59 $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Each" from LINEAR CORRELATION→LINEAR CORRELATION — all question types→Statistics STD 12 Commerce question papers→Gujarat Board STD 12 Commerce question papers→Gujarat Board question paper generator→

Similar questions

Find the value of $\lim _{x \rightarrow 1} \frac{\sqrt{x+3}-2}{\sqrt{x+8}-3}$
→
A normal distribution has mean $52$ and variance $64.$ Obtain estimated limits which include exactly middle $25\%$ of the observations.
→
$X$ is a Binomial variate. If $n=5$ and $p=\frac{1}{3}$, find the Binomial probabilities of possible values of $X$.
→
For a producer, the production cost function is $C=80-5 x+\frac{1}{4} x^{2}$. How much should be produced for minimum cost? Find the minimum cost.
→
For a Binomial variate $X, n=5$ and $p=0.5$. Find the following probabilities:$(1)\ P(0 \leq X<2)\ (2)\ P(X>3)\ (3)\ P(2 \leq X<4)$
→
The time taken by participants to complete the run in a
full marathon race follows normal distribution with
mean $5$ hours and standard deviation $0.8$ hours.
$(1)$ What will be the maximum time in the fastest running
$15 \%$ participants $?$
$(2)$ Out of $2000$ participants, how many would complete
their run in $6$ hours $?$
→
$\lim\limits_{x \rightarrow 0} \frac{f(2+x)-f(2-x)}{2 x}$ where $f(x)=x^2$
→
A balanced coin is tossed thrice. If the first two tosses have resulted in tail, find the probability that tall appears on the coin in all the three trials.
→
If $f(x)=x^{3}$ then find the value of $\lim _{h \rightarrow 0} \frac{f(3+h)-f(3-h)}{2 h} .$
→
An unbiased coin is tossed six times. Find the probability of getting $(1)\ 5$ heads, $(2)$ at the most $3$ heads.
→