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.

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 A frequency distribution shows how often each different value in a set of data occurs. A histogram is the most commonly used graph to show frequency distributions. The histogram for the given data is constructed as follows: The class 20 − 25 has the highest frequency, hence it is the modal class. We have to connect the endpoints from the modal class as shown in the histogram. The intersection points of these lines represents the mode, which comes out to be around 21 . 5 . Hence, mode of the daily pocket expenses is ₹ 21 . 5 .

The following distribution represents the height of 160 students of a school. Height (in cm) Number of students 140 - 145 12 145 - 150 20 150 - 155 30 155 - 160 38 160 - 165 24 165 - 270 16 170 - 180 12 175 - 180 8 Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, the interquartile range

Given, The following distribution represents the height of 160 students of a school. The table for the data given is Height (in cm) Number of students Cumulative frequency (Less than type) 140 - 145 12 12 145 - 150 20 32 150 - 155 30 62 155 - 160 38 100 160 - 165 24 124 165 - 170 16 140 170 - 175 12 152 175 - 180 8 160 Total N = 160 Take 2 cm = 10 height on the x -axis and 2 cm = 20 students on the y -axis. The graph between upper limit of the class intervals and cumulative frequency is Now, to find first quartile N 4 = 160 4 = 40 Draw a line y = 40 , parallel to x -axis which cuts the ogive at point J . Draw a perpendicular line from point J on the x -axis which cuts the x -axis at x = 29.Therefore, first quartile, Q 1 = 151 To find third quartile 3 N 4 = 160 x 3 4 = 120 Draw a line y = 120 , parallel to x -axis, which cuts the ogive at point M . Now, draw a perpendicular line from point M on the x -axis which cuts the x -axis at x = 172 . ∴ Third quartile, Q 3 = 172 Hence, inter quartile range = Q 3 - Q 1 = 172 - 151 = 21

Jitender Gupta and Divya Malik Solutions for Exercise 6: ARCHIVES (Last 8 Years)

Author:Jitender Gupta & Divya Malik

Jitender Gupta Mathematics Solutions for Exercise - Jitender Gupta and Divya Malik Solutions for Exercise 6: ARCHIVES (Last 8 Years)

Attempt the practice questions from Exercise 6: ARCHIVES (Last 8 Years) with hints and solutions to strengthen your understanding. All In One ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from Jitender Gupta and Divya Malik Solutions for Exercise 6: ARCHIVES (Last 8 Years) with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 8

The histogram adjacent represents the score obtained by $25$ students in a Mathematics mental test. Use the data to determine the modal class.

Question Image

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 13

Calculate the mean of the distribution given below using the shortcut method.

Marks	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$	$51 - 60$	$61 - 70$	$71 - 80$
Number of students	$2$	$6$	$10$	$12$	$9$	$7$	$4$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 15

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

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 17

Find the mean of the following distribution by step deviation method.

Class interval	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$10$	$6$	$8$	$12$	$5$	$9$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 21

The following distribution represents the height of $160$ students of a school.

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Draw an ogive for the given distribution taking $2 cm = 5 cm$ of height on one axis and $2 cm = 20$ students on the other axis.

Using the graph, determine the median height.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 21

The following distribution represents the height of $160$ students of a school.

Height (in cm)	Number of students
$140 - 145$	$12$
$145 - 150$	$20$
$150 - 155$	$30$
$155 - 160$	$38$
$160 - 165$	$24$
$165 - 270$	$16$
$170 - 180$	$12$
$175 - 180$	$8$

Draw an ogive for the given distribution taking $2 cm = 5 cm$ of height on one axis and $2 cm = 20$ students on the other axis.

Using the graph, the interquartile range

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 21

The following distribution represents the height of $160$ students of a school.

Question Image

Draw an ogive for the given distribution taking $2 cm = 5 cm$ of height on one axis and $2 cm = 20$ students on the other axis.

Using the graph, if above $172 cm$ is considered as the tall boys of the class. Find the number of boys in the class who are tall.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>ARCHIVES (Last 8 Years)>Q 22

Find the mean of the following frequency distribution by assumed method up to two decimal places.

Class interval	Frequency
$25 - 30$	$14$
$30 - 35$	$22$
$35 - 40$	$16$
$40 - 45$	$6$
$45 - 50$	$5$
$50 - 55$	$3$
$55 - 60$	$4$

Jitender Gupta and Divya Malik Solutions for Exercise 6: ARCHIVES (Last 8 Years)

Jitender Gupta Mathematics Solutions for Exercise - Jitender Gupta and Divya Malik Solutions for Exercise 6: ARCHIVES (Last 8 Years)

Questions from Jitender Gupta and Divya Malik Solutions for Exercise 6: ARCHIVES (Last 8 Years) with Hints & Solutions

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