In an art competition the marks obtained are given below. From the marks, find the mean. Marks 0 or greater than 0 10 or greater than 10 20 or greater than 20 30 or greater than 30 40 or greater than 40 50 or greater than 50 Number of competitors 40 36 22 11 2 0

Given that in an art competition the marks obtained are given below. Marks 0 or greater than 0 10 or greater than 10 20 or greater than 20 30 or greater than 30 40 or greater than 40 50 or greater than 50 Number of competitors 40 36 22 11 2 0 Class interval Mid-point x i Frequency f i cumulative frequency c . f x i f i 0 - 10 5 4 40 20 10 - 20 15 14 36 210 20 - 30 25 11 22 275 30 - 40 35 9 11 315 40 - 50 45 2 2 90 ∑ f i = 40 ∑ x i f i = 910 We know that Arithmetic mean = ∑ x i f i ∑ f i Thus, 910 40 = 22 . 75 Hence, the mean from the given frequency distribution table is 22 . 75 .

Solve from the statistical data given below: Find median Class interval 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 Frequency 5 6 15 10 5 4 3 2

Given that, Class interval 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 Frequency 5 6 15 10 5 4 3 2 Now, let prepare the cumulative frequency distribution table for the given data, Class interval Frequency f Cumulative frequency 5 - 10 5 5 10 - 15 6 5 + 6 = 11 15 - 20 15 11 + 15 = 26 20 - 25 10 26 + 10 = 36 25 - 30 5 36 + 5 = 41 30 - 35 4 41 + 4 = 45 35 - 40 3 45 + 3 = 48 40 - 45 2 48 + 2 = 50 N = ∑ f = 50 N 2 = 50 2 = 25 ∴ Median = l + N 2 - F f m × i , where l is the boundary of the median class, F is the cumulative frequency of the class preceding the median class, f m is the frequency of the median class, i is the length of the median class, N = Total frequency Here, l = 15 , F = 11 , f m = 15 , i = 20 - 15 = 5 , N = 50 On substituting the values, we get, Median = 15 + 25 - 11 15 × 5 = 15 + 4 . 67 = 19 . 67 (approx) Hence, the median for the given data is 19 . 67 (approx).

THIRD SUMMATIVE TEST

Author: Bidyut Guha Thakurta & Amitava Mitra

Bidyut Guha Thakurta Mathematics Solutions for Exercise - THIRD SUMMATIVE TEST

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Questions from THIRD SUMMATIVE TEST with Hints & Solutions

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 13

The external radius of a hollow sphere made of $1 c m$ thick lead sheet is $6 c m$ . By melting the sphere, a solid cylindrical rod of $2 c m$ radius is formed. What is the length of the rod ?

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 13

The upper surface of a metallic sphere is cut out in such a way that the curved surface of the new sphere is half the previous one. What will be the ratio of the volume of the cut-out portion and the remaining portion of the sphere ?

HARD

10th West Bengal Board

IMPORTANT

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

The angle of depression of the top and foot of a lamp post as seen from the roof of a house $11$ metre high are $30 °$ and $60 °$ . What is the height of the lamp post ?

HARD

10th West Bengal Board

IMPORTANT

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

From a point on a horizontal line lying in the same plane with the chimney if $50$ metres proceeded towards the chimney, the angle of elevation of the top becomes $60 °$ from $30 °$ . What is the height of the chimney ?

HARD

10th West Bengal Board

IMPORTANT

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

In an art competition the marks obtained are given below. From the marks, find the mean.

Marks	$0$ or greater than $0$	$10$ or greater than $10$	$20$ or greater than $20$	$30$ or greater than $30$	$40$ or greater than $40$	$50$ or greater than $50$
Number of competitors	$40$	$36$	$22$	$11$	$2$	$0$

HARD

10th West Bengal Board

IMPORTANT

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

Solve from the statistical data given below:

Find median

Class interval	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency	$5$	$6$	$15$	$10$	$5$	$4$	$3$	$2$

MEDIUM

10th West Bengal Board

IMPORTANT

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

In an Entrance Examination the frequency distribution of the marks obtained is given below, and from this find the mode.

Age (in years)	$16 - 18$	$18 - 20$	$20 - 22$	$22 - 24$	$24 - 26$
Number of candidates	$45$	$75$	$38$	$22$	$20$

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 4

$A B$ is the diameter of a circle with centre $O$ . $P$ is any point on the circumference of the circle. If $∠ P O A = 120 °$ , then find $∠ P B O$ .

THIRD SUMMATIVE TEST

Bidyut Guha Thakurta Mathematics Solutions for Exercise - THIRD SUMMATIVE TEST

Questions from THIRD SUMMATIVE TEST with Hints & Solutions

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