Draw an ogive by less than method for the following data: Number of rooms 1 2 3 4 5 6 7 8 9 10 Number of houses 4 9 22 28 24 12 8 6 5 2

We first prepare the cumulative frequency distribution table by less than method as given below, Number of rooms Number of houses Cumulative Frequency Less than or equal to 1 4 4 Less than or equal to 2 9 13 Less than or equal to 3 22 35 Less than or equal to 4 28 63 Less than or equal to 5 24 87 Less than or equal to 6 12 99 Less than or equal to 7 8 107 Less than or equal to 8 6 113 Less than or equal to 9 5 118 Less than or equal to 10 2 120 Now, we mark the upper class limits along x -axis and cumulative frequency along y -axis, thus we plot the points ( 1 , 4 ) , ( 2 , 13 ) , ( 3 , 35 ) , ( 4 , 63 ) , ( 5 , 87 ) , ( 6 , 99 ) , ( 7 , 107 ) , ( 8 , 113 ) , ( 9 , 118 ) and ( 10 , 120 ) .

The marks scored by 750 students in an examination are given in the form of a frequency distribution table: Marks Number of students 600 - 640 16 640 - 680 45 680 - 720 156 720 - 760 284 760 - 800 172 800 - 840 59 840 - 880 18 Prepare a cumulative frequency table by less than method and draw an ogive.

We first prepare the cumulative frequency table by less than method as given below: Marks Number of students Marks less than Cumulative frequency 600 - 640 16 640 16 640 - 680 45 680 61 680 - 720 156 720 217 720 - 760 284 760 501 760 - 800 172 800 673 800 - 840 59 840 732 840 - 880 18 880 750 Now, we mark the upper class limits along x -axis on a suitable scale and cumulative along y -axis on a suitable scale. Thus, we plot the points ( 640 , 16 ) , ( 680 , 61 ) , ( 720 , 217 ) , ( 760 , 501 ) , ( 800 , 673 ) , ( 840 , 732 ) and 880 , 750 .

Draw an ogive to represent the following frequency distribution: Class-interval Number of students 0 - 4 2 5 - 9 6 10 - 14 10 15 - 19 5 20 - 24 3

The given frequency distribution is not continuous. So, we first make it continuous and prepare the cumulative frequency distribution as under: Class-interval Number of students Upper class limits Cumulative frequency 0 - 4 . 5 2 Less than 4 . 5 2 4 . 5 - 9 . 5 6 Less than 9 . 5 8 9 . 5 - 14 . 5 10 Less than 14 . 5 18 14 . 5 - 19 . 5 5 Less than 19 . 5 23 19 . 5 - 24 . 5 3 Less than 24 . 5 26 Now, we mark the upper class limits or upper boundaries along x -axis and cumulative frequencies along y -axis. Thus, we plot the points ( 4 . 5 , 2 ) , ( 9 . 5 , 8 ) , ( 14 . 5 , 18 ) , ( 19 . 5 , 23 ) and 24 . 5 , 26 .

The monthly profits ( in ₹ ), of 100 shops are distributed as follows: Profits per shop No. of shops 0 - 50 12 50 - 100 18 100 - 150 27 150 - 200 20 200 - 250 17 250 - 300 6 Draw the frequency polygon for it.

We have, Profit per shop Mid-value No. of shops ( - 50 ) - 0 - 25 0 0 - 50 25 12 50 - 100 75 18 100 - 150 125 27 150 - 200 175 20 200 - 250 225 17 250 - 300 275 6 300 - 350 325 0 Now, we mark the mid-value along x -axis and number of shops along y -axis. Thus, we plot the points ( - 25 , 0 ) , ( 25 , 12 ) , ( 75 , 18 ) , ( 125 , 27 ) , ( 175 , 20 ) , ( 225 , 17 ) , ( 275 , 6 ) & ( 325 , 0 ) .

The following distribution given the daily income of 50 workers of a factory: Daily income (in ₹ ) Number of workers: 100 - 120 12 120 - 140 14 140 - 160 8 160 - 180 6 180 - 200 10 Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

We first prepare the cumulative frequency table by less than method as given below: Daily income (in ₹ ) Cumulative frequency Less than - 120 12 Less than - 140 26 Less than - 160 34 Less than - 180 40 Less than - 200 50 Now, we mark the upper-class limits along x -axis and cumulative frequencies along y -axis. Thus, we plot the points ( 120 , 12 ) , ( 140 , 26 ) , ( 160 , 34 ) , ( 180 , 40 ) & ( 200 , 50 ) .

The following table gives production yield per hectare of wheat of 100 farms of a village: Production yield in kg per hectare: 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Number of farms: 2 8 12 24 38 16 Draw 'less than' ogive and 'more than' ogive.

Less than method: We first prepare the cumulative frequency table by less than method as given below: Production yield (in kg per hectare) Number of farms Production yield less than Cumulative frequency 50 - 55 2 55 2 55 - 60 8 60 10 60 - 65 12 65 22 65 - 70 24 70 46 70 - 75 38 75 84 75 - 80 16 80 100 Now, mark the upper class limits on x -axis and cumulative frequencies along y -axis. We plot the points ( 55 , 2 ) , ( 60 , 10 ) , ( 65 , 22 ) , ( 70 , 46 ) , ( 75 , 84 ) and ( 80 , 100 ) . More than method: We prepare the cumulative frequency table by more than method as given below: Production yield (in kg per hectare) Number of farms Production yield more than Cumulative frequency 50 - 55 2 50 100 55 - 60 8 55 98 60 - 65 12 60 90 65 - 70 24 65 78 70 - 75 38 70 54 75 - 80 16 75 16 Now, mark the lower class limits on x -axis and cumulative frequencies along y -axis. We plot the points ( 50 , 100 ) , ( 55 , 98 ) , ( 60 , 90 ) , ( 65 , 78 ) , ( 70 , 54 ) and ( 75 , 16 ) .

During the medical check-up of 35 students of a class, their weights were recorded as follows: Daily income (in Rs) Cumulative frequency Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula.

Less than method: Now, mark the upper class limits on x -axis and cumulative frequencies along y -axis. We plot the points ( 38 , 0 ) , ( 40 , 3 ) , ( 42 , 5 ) , ( 44 , 9 ) , ( 46 , 14 ) , ( 48 , 28 ) , ( 50 , 32 ) & ( 52 , 35 ) . Weight (in kg) Number of students Weight less than Cumulative frequency 36 - 38 0 38 0 38 - 40 3 40 3 40 - 42 2 42 5 42 - 44 4 44 9 44 - 46 5 46 14 46 - 48 14 48 28 48 - 50 4 50 32 50 - 52 3 52 35 Now, mark the point A whose ordinate is N 2 = 35 2 = 17 . 5 . Its x -coordinate is 46 . 5 . So median of the given data is 46 . 5 . Verification: We have, Weight (in kg) Number of students Cumulative frequency 36 - 38 0 0 38 - 40 3 3 40 - 42 2 5 42 - 44 4 9 44 - 46 5 14 46 - 48 14 28 48 - 50 4 32 50 - 52 3 35 Now, N = 35 ⇒ N 2 = 35 2 = 17 . 5 The cumulative frequency just greater than 17 . 5 is 28 and the corresponding class is 46 - 48 . Thus, 46 - 48 is the median class such that. l = 46 , f = 14 , cf = 14 & h = 2 . ∴ Median = l + N 2 - cf f × h = 46 + 17 . 5 - 14 14 × 2 = 46 + 3 . 5 14 × 2 = 46 + 7 14 = 46 + 0 . 5 = 46 . 5 ⇒ Median = 46 . 5 kg Hence, verified.

HARD

10th CBSE

IMPORTANT

Earn 100

The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares): $1 - 3$ $3 - 5$ $5 - 7$ $7 - 9$ $9 - 11$ $11 - 13$

Number of families: $20$ $45$ $80$ $55$ $40$ $12$

Find the modal agricultural holdings of the village. If modal agricultural holdings of the village is $k$ hectares rounded off to one decimal place then write $k$ .

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Important Questions on Statistics

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.5>Q 19

The monthly income of $100$ families are given as below:

Income in (in $₹$ )	Number of families
$0 - 5000$	$8$
$5000 - 10000$	$26$
$10000 - 15000$	$41$
$15000 - 20000$	$16$
$20000 - 25000$	$3$
$25000 - 30000$	$3$
$30000 - 35000$	$2$
$35000 - 40000$	$1$

Calculate the modal income.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 1

Draw an ogive by less than method for the following data:

Number of rooms	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
Number of houses	$4$	$9$	$22$	$28$	$24$	$12$	$8$	$6$	$5$	$2$

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 2

The marks scored by

750

students in an examination are given in the form of a frequency distribution table:

Marks	Number of students
$600 - 640$	$16$
$640 - 680$	$45$
$680 - 720$	$156$
$720 - 760$	$284$
$760 - 800$	$172$
$800 - 840$	$59$
$840 - 880$	$18$

Prepare a cumulative frequency table by less than method and draw an ogive.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 3

Draw an ogive to represent the following frequency distribution:

Class-interval	Number of students
$0 - 4$	$2$
$5 - 9$	$6$
$10 - 14$	$10$
$15 - 19$	$5$
$20 - 24$	$3$

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 4

The monthly profits ( in $₹$ ), of $100$ shops are distributed as follows:

Profits per shop	No. of shops
$0 - 50$	$12$
$50 - 100$	$18$
$100 - 150$	$27$
$150 - 200$	$20$
$200 - 250$	$17$
$250 - 300$	$6$

Draw the frequency polygon for it.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 5

The following distribution given the daily income of $50$ workers of a factory:

Daily income (in $₹$ )	Number of workers:
$100 - 120$	$12$
$120 - 140$	$14$
$140 - 160$	$8$
$160 - 180$	$6$
$180 - 200$	$10$

Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 6

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

Production yield in kg per hectare:	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Number of farms:	$2$	$8$	$12$	$24$	$38$	$16$

Draw 'less than' ogive and 'more than' ogive.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 15 - Statistics>EXERCISE 15.6>Q 7

During the medical check-up of $35$ students of a class, their weights were recorded as follows:

Daily income (in Rs)	Cumulative frequency
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula.

Area of land (in hectares):	$1 - 3$	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$
Number of families:	$20$	$45$	$80$	$55$	$40$	$12$

Important Questions on Statistics

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