Draw a less than Ogive from the following frequency distribution: Marks 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 No. of students 3 7 13 25 40 14 10 From the curve find out median.

Less than type cumulative frequency distribution is, Marks Cumulative frequency c f Point Less than 5 3 ( 5 , 3 ) Less than 10 10 ( 10 , 10 ) Less than 15 23 ( 15 , 23 ) Less than 20 48 ( 20 , 48 ) Less than 25 88 ( 25 , 88 ) Less than 30 102 ( 30 , 102 ) Less than 35 112 ( 35 , 112 ) Here, N = 112 . So, N 2 = 56 . The graph we get, The value N 2 = 56 is marked on y - axis and a line parallel to x - axis is drawn. This line meets the curve at P . From P draw a perpendicular P N to meet x - axis at median 21 . Hence, the median of the frequency distribution is 21 .

Draw a less than Ogive from the following frequency distribution: Pocket expenses 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 No. of students 10 16 30 42 50 30 16 12 Find out the median from the curve.

Less than type cumulative frequency distribution is, Pocket expenses No. of students ( f ) Cumulative frequency ( c f ) Point 0 - 5 10 10 ( 5 , 10 ) 5 - 10 16 26 ( 10 , 26 ) 10 - 15 30 56 ( 15 , 56 ) 15 - 20 42 98 ( 20 , 98 ) 20 - 25 50 148 ( 25 , 148 ) 25 - 30 30 178 ( 30 , 1780 30 - 35 16 194 ( 32 , 194 ) 35 - 40 12 206 ( 40 , 206 ) Here, N = 206 . So, N 2 = 103 . So, the graph we get The value N 2 = 103 is marked on y - axis and a line parallel to x - axis is drawn. This line meets the curve at P . From P draw a perpendicular P N to meet x - axis at median 20 . 5 . Hence, the median of the frequency distribution is 20 . 5 .

Draw a less than Ogive from the following frequency distribution. Expenditure 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350 350 - 400 400 - 450 450 - 500 Number of workers 25 40 33 28 30 22 16 8

Less than type cumulative frequency distribution is, Expenditure Cumulative frequency ( c f ) Point l e s s t h a n 150 25 ( 150 , 25 ) l e s s t h a n 200 65 ( 200 , 65 ) l e s s t h a n 250 98 ( 250 , 98 ) l e s s t h a n 300 126 ( 300 , 126 ) l e s s t h a n 350 156 ( 350 , 156 ) l e s s t h a n 400 178 ( 400 , 178 ) l e s s t h a n 450 194 ( 450 , 194 ) l e s s t h a n 500 202 ( 500 , 202 ) Here, consider upper limits and plot them on x - axis and plot cumulative frequency on y - axis. So the graph we get is:

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 .

HARD

10th CBSE

IMPORTANT

Earn 100

The daily expenditure of $100$ families are given as under:

Expenditure $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$

Number of families $14$ $?$ $27$ $?$ $15$

The median and mode for the distribution are $₹ 26.67$ and $₹ 29$ respectively. Calculate the missing frequencies.

Important Questions on Statistics

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 1

Draw a less than Ogive from the following frequency distribution:

Marks	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
No. of students	$3$	$56 + x + y = 100$	$13$	$25$	$40$	$14$	$10$

From the curve find out median.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 2

Draw a less than Ogive from the following frequency distribution:

Pocket expenses	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
No. of students	$10$	$16$	$30$	$42$	$50$	$30$	$16$	$12$

Find out the median from the curve.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 3

Draw a less than Ogive from the following frequency distribution.

Expenditure	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$	$350 - 400$	$400 - 450$	$450 - 500$
Number of workers	$25$	$40$	$33$	$28$	$30$	$22$	$16$	$8$

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	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$
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	$8$	$18$	$23$	$37$	$47$	$27$	$16$	$7$

The daily expenditure of 100 families are given as under: Expenditure 0-10 10-20 20-30 30-40 40-50 Number of families 14 ? 27 ? 15 The median and mode for the distribution are ₹26.67 and ₹29 respectively. Calculate the missing frequencies.

Important Questions on Statistics

Learn and Prepare for any exam you want !

The daily expenditure of $100$ families are given as under:

Expenditure $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$

Number of families $14$ $?$ $27$ $?$ $15$

The median and mode for the distribution are $₹ 26.67$ and $₹ 29$ respectively. Calculate the missing frequencies.