Draw a histogram from the following frequency distribution and find the mode from the graph: Class 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 Frequency 2 5 18 14 8 5

Steps of construction: ( i ) Take the scale along x - axis as 2 cm = 5 units , and along y - axis as 1 cm = 2 units . ( i i ) Construct the rectangles according to the data given in the question. The required histrogram is as shown in the figure above. ( i i i ) In the highest rectangle, draw two straight lines AC and BD from the corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. ( i v ) Let P be the point of intersection of the lines AC and BD . ( v ) Through the point P , draw a vertical line that meets the x - axis at point M . The abscissa of the point M represents the value 14 . ∴ The required mode = 14

A Mathematics aptitude test of 50 students are recorded as follows: Marks 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of students 4 8 14 19 5 Draw a histogram for the above data using a graph paper and locate the mode.

Given, Steps of construction: ( i ) Take the scale along x - axis as 2 cm = 10 units , and along y - axis as 1 cm = 2 units . ( i i ) Since the scale on x - axis starts at 50 , a break, known as kink, is drawn near to the origin along the x - axis to indicate that the graph is drawn to scale beginning at 50 on the x - axis, and not at the origin itself. ( i i i ) Construct the rectangles according to the data given in the question. The required histogram is as shown in the figure above. ( i v ) In the highest rectangle, draw two straight lines AC and BD from the corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. ( v ) Let P be the point of intersection of the lines AC and BD . ( v i ) Through the point P , draw a vertical line that meets the x - axis at point M . The abscissa of the point M represents the value 82 . 5 . ∴ The required modal marks = 82 . 5 marks .

Draw a histogram and estimate the mode for the following frequency distribution: Classes 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 2 8 10 5 4 3

Given, Steps of construction: ( i ) Take the scale along x - axis as 2 cm = 10 units , and along y - axis as 1 cm = 1 unit . ( i i ) Construct the rectangles according to the data given in the question. The required histogram is as shown in the figure above. ( i i i ) In the highest rectangle, draw two straight lines AC and BD from the corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. ( i v ) Let P be the point of intersection of the lines AC and BD . ( v ) Through the point P , draw a vertical line that meets the x - axis at point M . The abscissa of the point M represents the value 23 . ∴ The required mode = 23

Using a graph paper, draw a histogram for the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data: Runs scored 3000 - 4000 4000 - 5000 5000 - 6000 6000 - 7000 7000 - 8000 8000 - 9000 9000 - 10000 Number of batsmen 4 18 9 6 7 2 4

Given, Steps of construction: ( i ) Take the scale along x - axis as 2 cm = 1000 units , and along y - axis as 1 cm = 2 units . ( i i ) Since the scale on x - axis starts at 3000 , a break, known as kink, is drawn near to the origin along the x - axis to indicate that the graph is drawn to scale beginning at 3000 on the x - axis, and not at the origin itself. ( i i i ) Construct the rectangles according to the data given in the question. The required histogram is as shown in the figure above. ( i v ) In the highest rectangle, draw two straight lines AC and BD from the corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. ( v ) Let P be the point of intersection of the lines AC and BD . ( v i ) Through the point P , draw a vertical line that meets the x - axis at point M . The abscissa of the point M represents the value 4600 . ∴ The required modal runs = 4600 runs .

Use a graph paper for this question. The daily pocket expenses of 200 students in a school are given below: Pocket expenses (in ₹ ) 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 Number of students (frequency) 10 14 28 42 50 30 14 12 Draw a histogram representing the above distribution and estimate the mode from the graph.

Given, Steps of construction: ( i ) Take the scale along x - axis as 2 cm = 5 units , and along y - axis as 1 cm = 5 units . ( i i ) Construct the rectangles according to the data given in the question. The required histogram is as shown in the figure above. ( i i i ) In the highest rectangle, draw two straight lines AC and BD from the corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. ( i v ) Let P be the point of intersection of the lines AC and BD . ( v ) Through the point P , draw a vertical line that meets the x - axis at point M . The abscissa of the point M represents the value 21 . 50 . ∴ The required modal pocket expenses = ₹ 21 . 50

Draw a histogram for the following distribution: Wt. (in kg ) 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 65 - 69 Number of students 2 8 12 10 6 4 Hence, estimate the modal weight.

We have to make the given discontinuous distribution as continuous one. Adjustment factor = 45 - 44 2 = 1 2 = 0 . 5 ∴ The adjusted continuous frequency distribution would be: Wt. (in kg ) 39 . 5 - 44 . 5 44 . 5 - 49 . 5 49 . 5 - 54 . 5 54 . 5 - 59 . 5 59 . 5 - 64 . 5 64 . 5 - 69 . 5 Number of students 2 8 12 10 6 4 Steps of construction: ( i ) Take the scale along x - axis as 2 cm = 5 units , and along y - axis as 1 cm = 1 unit . ( i i ) Since the scale on x - axis starts at 39 . 5 , a break, known as kink, is drawn near to the origin along the x - axis to indicate that the graph is drawn to scale beginning at 39 . 5 on the x - axis, and not at the origin itself. ( i i i ) Construct the rectangles according to the data given in the question. The required histogram is as shown in the figure above. ( i v ) In the highest rectangle, draw two straight lines AC and BD from the corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. ( v ) Let P be the point of intersection of the lines AC and BD . ( v i ) Through the point P , draw a vertical line that meets the x - axis at point M . The abscissa of the point M represents the value 52 . 75 . ∴ The required modal weight = 52 . 75 kg .

Find the mode of the following frequency distribution by drawing a histogram. Mid values 12 18 24 30 36 42 48 Frequency 20 12 8 24 16 8 12

Given, data Mid-values 12 18 24 30 36 42 48 Frequency 20 12 8 24 16 8 12 From mid-value (class mark) we find out the class interval. Difference bw second mid-value and first mid-value ⇒ 18 - 12 = 6 = h (Let assume) (ii) ∴ h 2 = 6 2 = 3 For lower limit, minutes 3 from mid-value and for upper limit, add 3 for mid-value. Class mark Frequency Class interval 12 20 9 - 15 18 12 15 - 21 24 8 21 - 27 30 24 27 - 33 36 16 33 - 39 42 8 39 - 45 48 12 45 - 51 According to the given data, make a bar graph as follows. Join the corner of the bar from both the sides, which meets at P . From this point draw perpendicular to x - axis , meeting x-axis at Q . Measure the value of Q = 31 Hence, from the bar-graph we have the mode as 31 .

M L Aggarwal Solutions for Exercise 4: Exercise 21.4

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 4: Exercise 21.4

Attempt the practice questions from Exercise 4: Exercise 21.4 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Exercise 4: Exercise 21.4 with Hints & Solutions

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 1

Draw a histogram from the following frequency distribution and find the mode from the graph:

Class	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
Frequency	$2$	$5$	$18$	$14$	$8$	$5$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 2

A Mathematics aptitude test of $50$ students are recorded as follows:

Marks	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students	$4$	$8$	$14$	$19$	$5$

Draw a histogram for the above data using a graph paper and locate the mode.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 3

Draw a histogram and estimate the mode for the following frequency distribution:

Classes	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$2$	$8$	$10$	$5$	$4$	$3$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 4

Using a graph paper, draw a histogram for the given distribution showing the number of runs scored by $50$ batsmen. Estimate the mode of the data:

Runs scored	$3000 - 4000$	$4000 - 5000$	$5000 - 6000$	$6000 - 7000$	$7000 - 8000$	$8000 - 9000$	$9000 - 10000$
Number of batsmen	$4$	$18$	$9$	$6$	$7$	$2$	$4$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 5

Use a graph paper for this question. The daily pocket expenses of $200$ students in a school are given below:

Pocket expenses (in $₹$ )	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
Number of students (frequency)	$10$	$14$	$28$	$42$	$50$	$30$	$14$	$12$

Draw a histogram representing the above distribution and estimate the mode from the graph.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 6

Draw a histogram for the following distribution:

Wt. (in $kg$ )	$40 - 44$	$45 - 49$	$50 - 54$	$55 - 59$	$60 - 64$	$65 - 69$
Number of students	$2$	$8$	$12$	$10$	$6$	$4$

Hence, estimate the modal weight.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.4>Q 7

Find the mode of the following frequency distribution by drawing a histogram.

Mid values	$12$	$18$	$24$	$30$	$36$	$42$	$48$
Frequency	$20$	$12$	$8$	$24$	$16$	$8$	$12$

M L Aggarwal Solutions for Exercise 4: Exercise 21.4

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 4: Exercise 21.4

Questions from M L Aggarwal Solutions for Exercise 4: Exercise 21.4 with Hints & Solutions

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