Draw more than Ogive from the following frequency distribution. Class - interval 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350 Frequency 4 6 13 5 2 Find the median from the curve.

More than type cumulative frequency distribution is, Class Interval f Cumulative frequency ( c f ) Point 100 - 150 4 30 ( 100 , 30 ) 150 - 200 6 26 ( 150 , 26 ) 200 - 250 13 20 ( 200 , 20 ) 250 - 300 5 7 ( 250 , 7 ) 300 - 350 2 2 ( 300 , 2 ) Here, N = 30 . So, N 2 = 15 . So, the graph we get The value N 2 = 15 is marked on y - axis and a line parallel to x - axis is drawn. This line meets the curve at a point. From that point draw a perpendicular to meet x - axis at median 219 . 2 . Hence, the median of the frequency distribution is 219 . 2 .

Draw an Ogive for the following frequency distribution by greater than method. Marks less than less than 10 less than 20 less than 30 less than 40 less than 50 less than 60 Number of students 7 10 23 51 66 73 From the curve find out median.

Here, less than type distribution is given. So more than type cumulative frequency distribution is, Marks No of students Cumulative frequency Points 0 - 10 7 73 0 , 73 10 - 20 ( 10 - 7 ) = 3 66 10 , 66 20 - 30 ( 23 - 10 ) = 13 63 20 , 63 30 - 40 ( 51 - 23 ) = 28 50 30 , 50 40 - 50 ( 66 - 51 ) = 15 22 40 , 22 50 - 60 ( 73 - 66 ) = 7 7 50 , 7 So, the graph we get Here, N = 73 which is odd, so we need find N + 1 2 . The value N + 1 2 = 73 + 1 2 = 37 is marked on y - axis and a line parallel to x - axis is drawn. This line meets the curve at a point. From that point draw a perpendicular to meet x - axis at median 34 . 8 . Hence, the median of the frequency distribution is 34 . 8 .

For the data given below, "less than and greater than Ogive" and hence find the value of median. Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No.of students 4 6 14 16 14 8 16 5 12 10

For less than Ogive curve, cumulative frequency table is, Marks Less than point Number of students f Cumulative frequency c f Point 0 - 10 10 4 4 ( 10 , 4 ) 10 - 20 20 6 10 ( 20 , 10 ) 20 - 30 30 14 24 ( 30 , 24 ) 30 - 40 40 16 40 ( 40 , 40 ) 40 - 50 50 14 54 ( 50 , 54 ) 50 - 60 60 8 62 ( 60 , 62 ) 60 - 70 70 16 78 ( 70 , 78 ) 70 - 80 80 5 83 ( 80 , 83 ) 80 - 90 90 12 95 ( 90 , 95 ) 90 - 100 100 10 105 ( 100 , 105 ) For greater than Ogive curve, the cumulative frequency table is, Marks Less than point Number of students f Cumulative frequency c f Point 0 - 10 90 10 10 ( 90 , 10 ) 10 - 20 80 12 22 ( 80 , 22 ) 20 - 30 70 5 27 ( 70 , 27 ) 30 - 40 60 16 43 ( 60 , 43 ) 40 - 50 50 8 51 ( 50 , 51 ) 50 - 60 40 14 65 ( 40 , 65 ) 60 - 70 30 16 81 ( 30 , 81 ) 70 - 80 20 14 95 ( 20 , 95 ) 80 - 90 10 6 101 ( 10 , 101 ) 90 - 100 0 4 105 ( 0 , 105 ) So, the graph we get is, Here, the two curves intersect at 50 , 54 . So, the x - axis point is 50 . Hence, the median is 50 .

For the data given below, draw "Less than and greater than Ogive" and hence, find the value of median. Production (in tons) 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 80 - 90 No. of labourers 8 18 23 37 47 27 16 7

For less than Ogive the cumulative frequency table is, Production (in tons) Less than point No. of labourers ( f ) Cumulative frequency ( c f ) point 0 - 10 10 8 8 ( 10 , 8 ) 10 - 20 20 18 26 ( 20 , 26 ) 20 - 30 30 23 49 ( 30 , 49 ) 30 - 40 40 37 86 ( 40 , 86 ) 40 - 50 50 47 133 ( 50 , 133 ) 50 - 60 60 26 159 ( 60 , 159 ) 60 - 70 70 16 175 ( 70 , 175 ) 70 - 80 80 7 182 ( 80 , 182 ) For greater than Ogive, the cumulative frequency table is, Production (in tons) Less than point No. of labourers ( f ) Cumulative frequency ( c f ) point 0 - 10 70 7 7 ( 70 , 7 ) 10 - 20 60 16 23 ( 60 , 23 ) 20 - 30 50 26 49 ( 50 , 49 ) 30 - 40 40 47 96 ( 40 , 96 ) 40 - 50 30 37 133 ( 30 , 133 ) 50 - 60 20 23 156 ( 20 , 156 ) 60 - 70 10 18 174 ( 10 , 174 ) 70 - 80 0 8 182 ( 0 , 182 ) Plotting the cumulative frequency on y - axis and plot class limits on x - axis, we get So, the median is the point of intersection of these two curves. Here, if we draw a perpendicular from the intersection point on x - axis, we get 41 . Hence, the median is 41 .

Draw the Ogives for the following frequency distribution. And find median from the curves. Marks 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 No. of students 9 42 61 140 260 102 7 23 2

For less than Ogive, the cumulative frequency table is, Marks Less than point c f Point 0 - 9 9 9 ( 9 , 9 ) 10 - 19 19 51 ( 19 , 51 ) 20 - 29 29 112 ( 29 , 112 ) 30 - 39 39 252 ( 39 , 252 ) 40 - 49 49 512 ( 49 , 512 ) 50 - 59 59 614 ( 59 , 614 ) 60 - 69 69 621 ( 69 , 621 ) 70 - 79 79 644 ( 79 , 644 ) 80 - 89 89 646 ( 89 , 646 ) For greater than Ogive, the cumulative frequency table is, Marks Greater than point c f Point 0 - 9 0 646 ( 0 , 646 ) 10 - 19 10 637 ( 10 , 637 ) 20 - 29 20 595 ( 20 , 595 ) 30 - 39 30 534 ( 30 , 534 ) 40 - 49 40 394 ( 40 , 394 ) 50 - 59 50 134 ( 50 , 134 ) 60 - 69 60 32 ( 60 , 32 ) 70 - 79 70 25 ( 70 , 25 ) 80 - 89 80 2 ( 80 , 2 ) We plot the cumulative frequency on y - axis and limit of the class on x - axis, and we get Now, the point of intersection of this two curves is the median. Here, if we draw a perpendicular from the intersection point to x - axis, we get 42 . Hence, the median is 42 .

Draw two Ogives from the following frequency distribution. And find median from the curves. Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 4 10 16 22 20 18 8 2

For less than Ogive, the cumulative frequency table is Marks Less than point c f Point 0 - 10 10 4 ( 10 , 4 ) 10 - 20 20 14 ( 20 , 14 ) 20 - 30 30 30 ( 30 , 30 ) 30 - 40 40 52 ( 40 , 52 ) 40 - 50 50 72 ( 50 , 72 ) 50 - 60 60 90 ( 60 , 90 ) 60 - 70 70 98 ( 70 , 98 ) 70 - 80 80 100 ( 80 , 100 ) For greater than Ogive, the cumulative frequency table is Marks Greater than point c f Point 0 - 10 0 100 ( 0 , 100 ) 10 - 20 10 96 ( 10 , 96 ) 20 - 30 20 86 ( 20 , 86 ) 30 - 40 30 70 ( 30 , 70 ) 40 - 50 40 48 ( 40 , 48 ) 50 - 60 50 28 ( 50 , 28 ) 60 - 70 60 10 ( 60 , 10 ) 70 - 80 70 2 ( 70 , 2 ) Now plot the cumulative frequency on the y - axis and class limit on the x - axis, we get The intersection point of two curves is the median. Here, if we draw a perpendicular from the intersection point to the x - axis, we get 39 . Hence, the median is 39 .

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 6: EXERCISE

Author:H K Dass, Rama Verma & Bhagwat Swarup Sharma

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 6: EXERCISE

Attempt the free practice questions on Chapter 14: Statistics, Exercise 6: EXERCISE with hints and solutions to strengthen your understanding. New Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 6: EXERCISE with Hints & Solutions

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 4

Draw more than Ogive from the following frequency distribution.

Class - interval	$100 - 150$	$150 - 200$	$y -$	$250 - 300$	$219.2$
Frequency	$4$	$6$	$13$	$5$	$2$

Find the median from the curve.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 5

Draw a cumulative frequency curve for the following frequency distribution by greater than Ogive method also find the median from the curve.

Weight(in kg)	$40 - 44$	$44 - 48$	$48 - 52$	$52 - 56$	$56 - 60$	$60 - 64$	$64 - 68$
No.of students	$7$	$12$	$33$	$47$	$20$	$11$	$5$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 6

Draw an Ogive for the following frequency distribution by greater than method.

Marks less than	less than $10$	less than $20$	less than $30$	less than $40$	less than $50$	less than $60$
Number of students	$7$	$10$	$23$	$51$	$66$	$73$

From the curve find out median.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 7

For the data given below, "less than and greater than Ogive" and hence find the value of median.

Marks	$0 - 10$	$10 - 20$	$\begin{array}{c} 20 - 30 \end{array}$	$\begin{array}{c} 30 - 40 \end{array}$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No.of students	$4$	$6$	$14$	$16$	$14$	$8$	$16$	$5$	$12$	$10$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 8

For the data given below, draw "Less than and greater than Ogive" and hence, find the value of median.

Production (in tons)	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$80 - 90$
No. of labourers	$8$	$18$	$23$	$37$	$47$	$27$	$16$	$7$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 9

Draw the Ogives for the following frequency distribution. And find median from the curves.

Marks	0-9	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89
No. of students	9	42	61	140	260	102	7	23	2

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 10

Draw two Ogives from the following frequency distribution. And find median from the curves.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$4$	$10$	$16$	$22$	$20$	$18$	$8$	$2$

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 11

If the mode of a series is $600$ and median is $800$ , find the mean.

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 6: EXERCISE

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 6: EXERCISE

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 6: EXERCISE with Hints & Solutions

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