NCERT Class 9 Solutions: Statistics (Chapter 14) Exercise 14.3-Part 3

Glide to success with Doorsteptutor material for UGC Public-Administration: fully solved questions with step-by-step explanation- practice your way to success.

Q-7 The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Runs scored by two teams in cricket match

Number of balls

Teams A

Team B

2

5

1

6

8

2

9

10

4

5

5

6

6

3

10

4

6

8

2

10

Represent the table data of both the teams on the same graph by frequency polygons.

[Hint: First make the class intervals continuous.]

Solution:

Convert to continuous frequency distribution:

Difference between lower limit of class and upper limit of preceding class:

Hence, added to each upper class limit and subtract from the lower class limits.

Class marks

Obtain distribution is given as under:

Obtain continuous frequency distribution

Number of balls

Class marks

Team A

Team B

3.5

2

5

9.5

1

6

15.5

8

2

21.5

9

10

27.5

4

5

33.5

4

5

39.5

6

3

45.5

10

4

51.5

6

8

57.5

2

10

Class mark on x-axis and number of balls on y-axis

Drawn the graph:

{"chart":{"plotBackgroundColor":null,"plotShadow":true,"backgroundColor":"transparent","width":600},"title":{"text":"Number of balls Vs Runs scored"},"tooltip":{"pointFormat":"{series.name}: {point.y}"},"credits":{"enabled":false},"xAxis":{"type":"category","categories":["3.5","9.5","15.5","21.5","27.533.5","39.5","45.5","51.5","57.5","63.5"],"title":{"text":"Number of balls"}},"yAxis":{"type":"linear","title":{"text":"Runs scored"},"stackLabels":{"enabled":true,"style":{"fontWeight":"bold","color":"gray"}}},"plotOptions":{"series":{"allowPointSelect":true,"cursor":"pointer"}},"legend":{"floating":false,"backgroundColor":"white","borderColor":"silver","borderWidth":1,"shadow":true,"align":"right"},"series":[{"type":"line","name":"Team A","data":[2,1,8,9,4,5,6,10,6,2],"colors":[{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#90ed7d"],[1,"rgb(68,161,49)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#f7a35c"],[1,"rgb(171,87,16)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#8085e9"],[1,"rgb(52,57,157)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#f15c80"],[1,"rgb(165,16,52)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#e4d354"],[1,"rgb(152,135,8)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#2b908f"],[1,"rgb(0,68,67)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#f45b5b"],[1,"rgb(168,15,15)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#91e8e1"],[1,"rgb(69,156,149)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#7cb5ec"],[1,"rgb(48,105,160)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#434348"],[1,"rgb(0,0,0)"]]}],"dataLabels":{"enabled":true,"style":{"color":"black"},"connectorColor":"silver"}},{"type":"line","name":"Team B","data":[5,6,2,10,5,6,3,4,8,10],"colors":[{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#90ed7d"],[1,"rgb(68,161,49)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#f7a35c"],[1,"rgb(171,87,16)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#8085e9"],[1,"rgb(52,57,157)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#f15c80"],[1,"rgb(165,16,52)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#e4d354"],[1,"rgb(152,135,8)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#2b908f"],[1,"rgb(0,68,67)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#f45b5b"],[1,"rgb(168,15,15)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#91e8e1"],[1,"rgb(69,156,149)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#7cb5ec"],[1,"rgb(48,105,160)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":1,"y2":0},"stops":[[0,"#434348"],[1,"rgb(0,0,0)"]]}],"dataLabels":{"enabled":true,"style":{"color":"black"},"connectorColor":"silver"}}]}
Number of ballsRuns scoredNumber of balls Vs Runs scored21894561062562105634810Team ATeam B3.59.515.521.527.533.539.545.551.557.563.502.557.51012.563.5Team B: 10

Q-8 A random survey of the number of children of various age groups playing in park was found as follows:

Draw a histogram to represent the data of table

Age (in years)

Number of children

5

3

6

12

9

10

4

Draw a histogram to represent the data above.

Solution:

As given frequency data in class size are different.

So, we calculate adjusted frequency for each class using formula:

Adjusted frequency

Here, minimum class size

Find the adjusted frequency to draw histogram

Age (In year)

Frequency (number of children)

Width of classes

Adjusted Frequency

5

1

3

1

6

2

12

2

9

3

10

5

4

2

In below chart age of children on x-axis

Proportion of children per 1 year interval on y-axis

{"chart":{"plotBackgroundColor":null,"plotShadow":true,"backgroundColor":"transparent","width":600},"title":{"text":"Age (in years) Vs Proportion of children per 1 year interval"},"tooltip":{"pointFormat":"{series.name}: {point.y}"},"credits":{"enabled":false},"xAxis":{"categories":["1-2","2-3","3-5","5-7","7-10","10-15","15-17"],"title":{"text":"Age (in years)"}},"yAxis":{"type":"linear","title":{"text":"Proportion of children per 1 year interval"},"stackLabels":{"enabled":true,"style":{"fontWeight":"bold","color":"gray"}}},"plotOptions":{"series":{"allowPointSelect":true,"cursor":"pointer"}},"legend":{"floating":false,"backgroundColor":"white","borderColor":"silver","borderWidth":1,"shadow":true,"align":"right"},"series":[{"type":"column","name":"Age (in years) Vs Proportion of children per 1 year interval","data":[5,3,3,6,3,2,2],"colors":[{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#91e8e1"],[1,"rgb(69,156,149)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#7cb5ec"],[1,"rgb(48,105,160)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#434348"],[1,"rgb(0,0,0)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#90ed7d"],[1,"rgb(68,161,49)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#f7a35c"],[1,"rgb(171,87,16)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#8085e9"],[1,"rgb(52,57,157)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#f15c80"],[1,"rgb(165,16,52)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#e4d354"],[1,"rgb(152,135,8)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#2b908f"],[1,"rgb(0,68,67)"]]},{"linearGradient":{"x1":0,"y1":0,"x2":0,"y2":1},"stops":[[0,"#f45b5b"],[1,"rgb(168,15,15)"]]}],"pointPadding":0,"groupPadding":0,"shadow":false}]}
Age (in years)Proportion of children per 1 year intervalAge (in years) Vs Proportion of children per 1 year intervalAge (in years) Vs Proportion of children per 1 year interval1-22-33-55-77-1010-1515-17024681-2Age (in years) Vs Proportion of children per 1 year interval: 5