From the data given below draw an ogive (greater than type) and from this find the median. Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of students (Frequency) 5 3 4 3 3 4 7 9 7 8

Given, Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of students (Frequency) 5 3 4 3 3 4 7 9 7 8 Convert the simple frequency to greater than type ogive. Class interval Cumulative frequency (more than) 0 - 10 48 + 5 = 53 10 - 20 45 + 3 = 48 20 - 30 41 + 4 = 45 30 - 40 38 + 3 = 41 40 - 50 35 + 3 = 38 50 - 60 31 + 4 = 35 60 - 70 24 + 7 = 31 70 - 80 15 + 9 = 24 80 - 90 8 + 7 = 15 90 - 100 8 In a graph plot points. Because N = 53 Therefore, N 2 = 53 2 = 26 . 5 . Though the line point ( 0 , 26 . 5 ) on the y - a x i s draw a line parallel to x - a x i s to meet ogive at P ,.From P draw perpendicular P M on O X . The abscissa of M is 66 ( A p p r o x . ) . Thus, the median is 66 ( a p p r o x )

The height and respective number of students of 50 students of class ten are given below. From this find median and mode. Height (in cm) 120 - 130 130 - 140 140 - 150 150 - 160 160 - 170 Number of students 2 8 12 20 8

Given The height and respective number of students of 50 students is given. Height (in cm) Number of students Cumulative Frequency 120 - 130 2 2 130 - 140 8 2 + 8 = 10 140 - 150 12 10 + 12 = 22 150 - 160 20 22 + 20 = 42 160 - 170 8 42 + 8 = 50 ∑ f = 50 The cumulative frequency of the class which is just greater than N 2 = 50 2 = 25 is 150 - 160 . Therefore , Median = l + N 2 - F f m × i = 150 + 50 2 - 22 20 × 10 = 150 + 25 - 22 20 × 10 = 150 + 1 . 5 = 151 . 5 Maximum frequency is 20 Mode = l + f m - f 1 2 f m - f 1 - f 2 × i Therefore model class is 150 - 160 = 150 + 20 - 12 2 × 20 - 12 - 8 × 10 = 150 + 8 20 × 10 = 150 + 4 = 154 Therefore, median is 151 . 5 c m and mode is 154 c m

HARD

10th West Bengal Board

IMPORTANT

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A cylindrical bowl whose base is hemispherical is open at upper end. The height of the cylindrical portion is $2$ metre and the inner radius of both hemisphere and the cylinder is $4$ decimeter. In how many times this bowl can be filled up by water by a cylindrical can of height $4 \frac{1}{4}$ decimeter and radius $1 \frac{1}{3}$ decimeter.

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Important Questions on Third Summative Test

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 14

A low land

40

meter long and

30

meter broad is to make

3

decimeter high. For this a drain

2.5

meter broad around the land is dug. Find the depth of the drain.

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 14

The height and radius of a right circular cylinder are

4.5

decimeter and

2

cm. By melting the cylinder

5

solids spheres of equal diameter are formed. What is the diameter of the spheres?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 15

From the data given below draw an ogive (greater than type) and from this find the median.

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students (Frequency)	$5$	$3$	$4$	$3$	$3$	$4$	$7$	$9$	$7$	$8$

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 15

The height and respective number of students of $50$ students of class ten are given below. From this find median and mode.

Height (in cm)	$120 - 130$	$130 - 140$	$140 - 150$	$150 - 160$	$160 - 170$
Number of students	$2$	$8$	$12$	$20$	$8$

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 1

Choose the correct answer :

In a partnership business Shyam invests $₹ 6000$ for $8$ months and Akbar invests $₹ 8000$ for $4$ months. The ratio of the profit of Shyam and Akbar in the business is _____.

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10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 1

Choose the correct answer :

The value of $k$ for which the roots of the equation $5 x^{2} - 2 k x + 5 = 0$ may be real and equal, is _____.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 1

Choose the correct answer :

The ratio of height and slant height of a cone is $4 : 5$ , then the ratio of the height and diameter of the cone is _____.

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10th West Bengal Board

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SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 1

Choose the correct answer :

Two circles with centres $P$ and $Q$ have diameters of measures $x$ and $3 x$ respectively. The two circles touch externally when the length of $P Q$ is
_____.

Important Questions on Third Summative Test

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