Draw a scatter diagram and indicate the nature of correlation-WheX - 10 - 20 - 30 - 40 - 50 - 60 - 70 - 80 lllhline Imathbf Y - 5 - 10 - 15 - 20 - 25 - 30 - 35 - 40 lilhlinelendarray

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Standard XI

Statistics

Types of Correlation and Scatter Chart

Draw a scatte...

Question

Draw a scatter diagram and indicate the nature of correlation.

$\begin{matrix} X & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 Y & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 \end{matrix}$

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Solution

The pair of points are (10,5), (20,10), (30,15), (40,20), (50,25), (60,30), (70,35) and (80,40).
Now, we plot the points on a graph paper which is shown below:

Interpretation The diagram indicates that there is perfect positive correlation between the values of the two variables X and Y.

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Q. Draw a histogram and frequency polygon to represent the following data.

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of Students	$12$	$22$	$35$	$40$	$60$	$52$	$40$	$30$	$5$

Q. Draw scatter diagram for the following data and interpret it:

$x$	$10$	$20$	$30$	$40$	$50$	$60$	$70$
$y$	$32$	$20$	$24$	$36$	$40$	$28$	$38$

The marks obtained by $40$ students of a class are given below :
$80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70,$
$10, 60, 50, 20, 70, 70, 30, 80, 40, 20, 80, 90,$ $50, 80,$
$60, 70, 40, 50, 60, 90, 60, 40, 40, 60$ , and $60$

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Q. Draw a histogram for the following table which represent the marks obtained by

100

students in an examination.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Number of students	$5$	$10$	$15$	$20$	$25$	$12$	$8$	$5$

Identify the modal class:

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Draw a scatter diagram and indicate the nature of correlation. X1020304050607080Y510152025303540

The pair of points are (10,5), (20,10), (30,15), (40,20), (50,25), (60,30), (70,35) and (80,40). Now, we plot the points on a graph paper which is shown below: Interpretation The diagram indicates that there is perfect positive correlation between the values of the two variables X and Y.

Draw a scatter diagram and indicate the nature of correlation.

$\begin{matrix} X & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 Y & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 \end{matrix}$

The pair of points are (10,5), (20,10), (30,15), (40,20), (50,25), (60,30), (70,35) and (80,40).
Now, we plot the points on a graph paper which is shown below:

Interpretation The diagram indicates that there is perfect positive correlation between the values of the two variables X and Y.