Find the median of the following data by making a 'less than ogive' Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of students 5 3 4 3 3 4 7 9 7 8

Marks Cumulative frequency Less than 10 5 Less than 20 8 Less than 30 12 Less than 40 15 Less than 50 18 Less than 60 22 Less than 70 29 Less than 80 38 Less than 90 45 Less than 100 53 We plot the points = ( 10 , 5 ) , ( 20 , 8 ) , ( 30 , 12 ) , ( 40 , 15 ) , ( 50 , 18 ) , ( 60 , 22 ) , ( 70 , 29 ) , ( 80 , 38 ) , ( 90 , 45 ) and ( 100 , 53 ) to get the less than type ogive as follows: Here, N = 53 ⇒ N 2 = 26 . 5 At y = 26 . 5 , affix A Through A , draw a horizontal line meeting the curve at P Through P , a vertical line is drawn which meets O X at M O M = 68 units Hence, median marks = 68 .

Draw a ‘more than’ ogive for the data given below which gives the marks of 100 students. Marks 0 – 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 No of Students 4 6 10 10 25 22 18 5

The frequency distribution table of more than type is as follows: Marks (upper class limits) Cumulative frequency ( c f ) More than 0 96 + 4 = 100 More than 10 90 + 6 = 96 More than 20 80 + 10 = 90 More than 30 70 + 10 = 80 More than 40 45 + 25 = 70 More than 50 23 + 22 = 45 More than 60 18 + 5 = 23 More than 70 5 Taking lower class limits of on x -axis and their respective cumulative frequencies on y -axis, its ogive can be drawn as follows:

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution: Monthly Consumption (in units) 140 – 160 160 – 180 180 – 200 200 – 220 220 – 240 240 – 260 260 - 280 Number of Families 3 8 15 40 50 30 10 Prepare a ‘more than type’ ogive for the given frequency distribution.

The frequency distribution table of more than type is as follows: Height (in cm ) (lower class limit) Cumulative frequency ( c f ) More than 140 3 + 153 = 156 More than 160 8 + 145 = 153 More than 180 15 + 130 = 145 More than 200 40 + 90 = 130 More than 220 50 + 40 = 90 More than 240 30 + 10 = 40 More than 260 10 Taking the lower class limits of on x -axis and their respective cumulative frequencies on y -axis, its ogive can be drawn as follows:

The following table gives the production yield per hectare of wheat of 100 farms of a village. Production Yield (kg/ha) 50 – 55 55 – 60 60 – 65 65 - 70 70 – 75 75 - 80 Number of farms 2 8 12 24 38 16 Change the distribution to a ‘more than type’ distribution and draw its ogive. Using ogive, find the median of the given data.

The frequency distribution table of more than type is as follows: Production yield (kg/ha) (lower class limits) Cumulative frequency ( c f ) More than 50 2 + 98 = 100 More than 55 8 + 90 = 98 More than 60 12 + 78 = 90 More than 65 24 + 54 = 78 More than 70 38 + 16 = 54 More than 75 16 Taking the lower class limits on x -axis and their respective cumulative on y -axis, its ogive can be drawn as follows Here, N = 100 ⇒ N 2 = 50 . Mark the point A whose ordinate is 50 and its x -coordinate is 70 . 5 . Thus, median of the data is 70 . 5 .

The table given below shows the weekly expenditures on food of some households in a locality Weekly expenditure (in Rs ) Number of house holds 100 – 200 5 200 - 300 6 300 – 400 11 400 - 500 13 500 – 600 5 600 – 700 4 700 – 800 3 800 – 900 2 Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.

The frequency distribution table of less than type is as follows: Weekly expenditure (in Rs ) (upper class limits) Cumulative frequency (cf) Less than 200 5 Less than 300 5 + 6 = 11 Less than 400 11 + 11 = 22 Less than 500 22 + 13 = 35 Less than 600 35 + 5 = 40 Less than 700 40 + 4 = 44 Less than 800 44 + 3 = 47 Less than 900 47 + 2 = 49 Taking the lower class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be obtained as follows Now, The frequency distribution table of more than type is as follows: Weekly expenditure (in Rs ) (lower class limits) Cumulative frequency ( c f ) More than 100 44 + 5 = 49 More than 200 38 + 6 = 44 More than 300 27 + 11 = 38 More than 400 14 + 13 = 27 More than 500 9 + 5 = 14 More than 600 5 + 4 = 9 More than 700 2 + 3 = 5 More than 800 2 Taking the lower class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be obtained as follows:

The marks obtained by 100 students of a class in an examination are given below: Marks Number of students 0 – 5 2 5 – 10 5 10 – 15 6 15 – 20 8 20 – 25 10 25 – 30 25 30 – 35 20 35 – 40 18 40 – 45 4 45 – 50 2 Draw cumulative frequency curves by using (i) ‘less than’ series and (ii) ‘more than’ series. Hence, find the median.

(i) From the given table, we may prepare the ‘less than’ frequency table as shown below: Marks Number of students Less than 5 2 Less than 10 7 Less than 15 13 Less than 20 21 Less than 25 31 Less than 30 56 Less than 35 76 Less than 40 94 Less than 45 98 Less than 50 100 We plot the points A ( 5 , 2 ) , B ( 10 , 7 ) , C ( 15 , 13 ) , D ( 20 , 21 ) , E ( 25 , 31 ) , F ( 30 , 56 ) , G ( 35 , 76 ) and H ( 40 , 94 ) , I ( 45 , 98 ) and J ( 50 , 100 ) . Join A B , B C , C D , D E , E F , F G , G H , H I , I J and J A with a free hand to get the curve representing the ‘less than type’ series. (ii) More than series: Marks Number of students More than 0 100 More than 5 98 More than 10 93 More than 15 87 More than 20 79 More than 25 69 More than 30 44 More than 35 24 More than 40 6 More than 45 2 Now, on the same graph paper, we plot the points ( 0 , 100 ) , ( 5 , 98 ) , ( 10 , 93 ) , ( 15 , 87 ) , ( 20 , 79 ) , ( 25 , 69 ) , ( 30 , 44 ) , ( 35 , 24 ) , ( 40 , 6 ) and ( 45 , 2 ) .Join with a free hand to get the ‘more than type’ series. The two curves intersect at point L . Draw L M ⊥ O X cutting the x -axis at M . Clearly, M = 29 . 5 Hence, Median = 29 . 5 .

From the following data, draw the two types of cumulative frequency curves and determine the median: Marks Frequency 140 – 144 3 144 – 148 9 148 – 152 24 152 – 156 31 156 – 160 42 160 – 164 64 164 – 168 75 168 – 172 82 172 – 176 86 176 – 180 34

(i) Less than series: Marks Number of students Less than 144 3 Less than 148 12 Less than 152 36 Less than 156 67 Less than 160 109 Less than 164 173 Less than 168 248 Less than 172 330 Less than 176 416 Less than 180 450 We plot the points A ( 144 , 3 ) , B ( 148 , 12 ) , C ( 152 , 36 ) , D ( 156 , 67 ) , E ( 160 , 109 ) , F ( 164 , 173 ) , G ( 168 , 248 ) and H ( 172 , 330 ) , I ( 176 , 416 ) and J ( 180 , 450 ) . Join A B , B C , C D , D E , E F , F G , G H , H I , I J and J A with a free hand to get the curve representing the ‘less than type’ series. (ii) More than series: Marks Number of students More than 140 450 More than 144 447 More than 148 438 More than 152 414 More than 156 383 More than 160 341 More than 164 277 More than 168 202 More than 172 120 More than 176 34 Now, on the same graph paper, we plot the points A 1 ( 140 , 450 ) , B 1 ( 144 , 447 ) , C 1 ( 148 , 438 ) , D 1 ( 152 , 414 ) , E 1 ( 156 , 383 ) , F 1 ( 160 , 277 ) , H 1 ( 168 , 202 ) , I 1 ( 172 , 120 ) and J 1 ( 176 , 34 ) . Join A 1 B 1 , B 1 C 1 , C 1 D 1 , D 1 E 1 , E 1 F 1 , F 1 G 1 , G 1 H 1 , H 1 I 1 and I 1 J 1 with a free hand to get the ‘more than type’ series. The two curves intersect at point L . Draw L M ⊥ O X cutting the x -axis at M . Clearly, M = 166 cm Hence, median = 166 cm .

R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: Exercise 18E

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: Exercise 18E

Attempt the free practice questions from Exercise 5: Exercise 18E with hints and solutions to strengthen your understanding. Secondary School Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: Exercise 18E with Hints & Solutions

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 1

Find the median of the following data by making a 'less than ogive'

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students	$P$	$3$	$M$	$O M = 68 units$	$3$	$4$	$7$	$9$	$7$	$8$

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 3

Draw a ‘more than’ ogive for the data given below which gives the marks of $100$ students.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
No of Students	$4$	$6$	$10$	$10$	$25$	$22$	$18$	$5$

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 5

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

Monthly Consumption (in units)	$140 - 160$	$160 - 180$	$180 - 200$	$200 - 220$	$220 - 240$	$240 - 260$	$260 - 280$
Number of Families	$3$	$8$	$15$	$40$	$50$	$30$	$10$

Prepare a ‘more than type’ ogive for the given frequency distribution.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 6

The following table gives the production yield per hectare of wheat of $100$ farms of a village.

Production Yield (kg/ha)	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Number of farms	$2$	$8$	$12$	$24$	$38$	$16$

Change the distribution to a ‘more than type’ distribution and draw its ogive. Using ogive, find the median of the given data.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 7

The table given below shows the weekly expenditures on food of some households in a locality

Weekly expenditure (in $Rs$ )	Number of house holds
$100 - 200$	$5$
$200 - 300$	$6$
$300 - 400$	$11$
$400 - 500$	$13$
$500 - 600$	$5$
$600 - 700$	$4$
$700 - 800$	$3$
$800 - 900$	$2$

Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 9

The marks obtained by $100$ students of a class in an examination are given below:

Marks	Number of students
$0 - 5$	$2$
$5 - 10$	$5$
$10 - 15$	$6$
$15 - 20$	$8$
$20 - 25$	$10$
$25 - 30$	$25$
$30 - 35$	$20$
$35 - 40$	$18$
$40 - 45$	$4$
$45 - 50$	$2$

Draw cumulative frequency curves by using (i) ‘less than’ series and (ii) ‘more than’ series. Hence, find the median.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 9

The marks obtained by $100$ students of a class in an examination are given below:

Marks	Number of students
$0 - 5$	$2$
$5 - 10$	$5$
$10 - 15$	$6$
$15 - 20$	$8$
$20 - 25$	$10$
$25 - 30$	$25$
$30 - 35$	$20$
$35 - 40$	$18$
$40 - 45$	$4$
$45 - 50$	$2$

Draw more than type cumulative frequency curve and find the median from it.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18E>Q 10

From the following data, draw the two types of cumulative frequency curves and determine the median:

Marks	Frequency
$140 - 144$	$3$
$144 - 148$	$9$
$148 - 152$	$24$
$152 - 156$	$31$
$156 - 160$	$42$
$160 - 164$	$64$
$164 - 168$	$75$
$168 - 172$	$82$
$172 - 176$	$86$
$176 - 180$	$34$

R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: Exercise 18E

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: Exercise 18E

Questions from R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: Exercise 18E with Hints & Solutions

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