The number of books in different shelves of a library are as follows: 30 , 32 , 28 , 24 , 20 , 25 , 38 , 37 , 40 , 45 , 16 , 20 19 , 24 , 27 , 30 , 32 , 34 , 35 , 42 , 27 , 28 , 19 , 34 , 38 , 39 , 42 , 29 , 24 , 27 , 22 , 29 , 31 , 19 , 27 , 25 28 , 23 , 24 , 32 , 34 , 18 , 27 , 25 , 37 , 31 , 24 , 23 43 , 32 , 28 , 31 , 24 , 23 , 26 , 36 , 32 , 29 , 28 , 21 Prepare a cumulative frequency distribution table using 45 - 49 as the last class interval.

The minimum and maximum numbers of books in shelves are 16 and 45 . The range is 45 - 16 = 29 Given that 45 - 49 is the last class-interval. So, the class size is 49 - 45 = 4 Now calculate Range Class - size = 29 4 = 7 . 25 Thus, the number of classes is 8 . The cumulative frequency distribution is the following: No.of Books No.of Shohes (Frequency) Cumulative Frequency 13 - 17 1 1 17 - 21 6 7 21 - 25 11 18 25 - 29 15 33 29 - 33 12 45 33 - 37 5 50 37 - 41 6 56 41 - 45 3 59 45 - 49 1 60

In the following grouped frequency distribution table class marks are given: Class marks 10 22 34 46 58 70 Frequency 6 14 20 21 9 5 Construct less than cumulative frequencies.

In the following grouped frequency distribution table class marks are given: Class marks 10 22 34 46 58 70 Frequency 6 14 20 21 9 5 Class size = 22 - 10 = 12 Now, 12 2 = 6 To construct the class intervals from the given data, we are going to subtract and add 6 in each class marks to find the lower limit and upper limit respectively. Class marks 10 22 34 46 58 70 Class intervals 4 ‐ 16 16 ‐ 28 28 ‐ 40 40 ‐ 52 52 ‐ 64 64 ‐ 76 The progressive sum of the frequencies from the first class to the upper boundary of a particular class is called less than cumulative frequency. Therefore, the required table is shown below: Class intervals Frequencies Less than cumulative frequencies 4 ‐ 16 6 Less than 16 6 16 ‐ 28 14 Less than 28 6 + 14 = 20 28 ‐ 40 20 Less than 40 20 + 20 = 40 40 ‐ 52 21 Less than 52 40 + 21 = 61 52 ‐ 64 9 Less than 64 61 + 9 = 70 64 ‐ 76 5 Less than 76 70 + 5 = 76

The weights (in Kg ) of 20 students of Barasat Gandhi Memorial High School are given below: 44 42 30 38 32 44 32 30 34 40 42 44 42 49 44 47 49 45 35 48 Prepare a grouped frequency distribution table (with less than type cumulative frequency distribution) by taking the class-intervals 30 - 35 , 35 - 40 , . . . . . . etc. using tally-marks.

The weights (in Kg ) of 20 students of Barasat Gandhi Memorial High School are given below: 44 42 30 38 32 44 32 30 34 40 42 44 42 49 44 47 49 45 35 48 We need to prepare a grouped frequency distribution table (with less than type cumulative frequency distribution) by taking the class-intervals 30 - 35 , 35 - 40 , . . . . . . etc. using tally-marks. Groped frequency distribution table of the weighs of 20 students of Gandhi Memorial High School, Barasat: Class-intervals (Marks obtained) Tally-marks Class-frequencies Less than type cumulative frequency 30 - 35 | | | | 5 5 35 - 40 | | 2 7 40 - 45 | | | | | | | 8 15 45 - 50 | | | | 5 20 Total = 20 Hence, the above obtained table is the frequency distribution table for the given raw data.

Yield of coconuts grown in a village by 15 farmers is as follows. Draw less than type ogive. Number of coconuts Cumulative frequency Less than 50 2 Less than 75 4 Less than 100 9 Less than 125 10 Less than 150 11 Less than 175 13 Less than 200 15

Given: Number of coconuts Cumulative frequency Less than 50 2 Less than 75 4 Less than 100 9 Less than 125 10 Less than 150 11 Less than 175 13 Less than 200 15 Now we will plot this “less than type” ogive on the graph from the table of the less than type ogive, we get Here, the line represents “less than type”.

The following graph illustrates the times taken by 112 people to complete a puzzle. The median is used to divide these people into two groups. Find the median time taken by each of the groups.

Given: Cumulative frequency curves enable us to find the median and quartiles from a set of grouped data. To find the median, we draw a horizontal line across from the frequency axis to the curve at the n 2 th value and then down to the x -axis to determine the median data point. Here, n = 112 So, n 2 th value is 56 th value. Draw a line across from 56 on the vertical axis( y -axis) until it hits the curve and then draw a line vertically down until it touches the horizontal axis( x -axis). This is the median Q 2 . Draw a line across from 28 and 84 on the vertical axis( y -axis) until it hits the curve and then draw a line vertically down until it touches the horizontal axis( x -axis). This is the median Q 1 and Q 3 respectively. Thus, lower group median 28 t h approx 2 . 8 minutes and upper group median 84 t h approx 6 . 4 minutes.

The ages (in years) of the first 30 people visiting the Gardens in Paris on a certain day are shown. 25 65 34 48 4 55 32 45 23 43 23 37 45 36 26 39 42 45 29 15 15 20 64 37 61 25 17 23 45 36 Construct a cumulative frequency curve.

Given data: 25 65 34 48 4 55 32 45 23 43 23 37 45 36 26 39 42 45 29 15 15 20 64 37 61 25 17 23 45 36 The class width is the difference between the maximum and the minimum possible values in a class interval. Let the class width be 10 and first class interval be 0 ≤ x < 10 . The cumulative frequency is the sum of the frequencies for every class, up to and including the current one. Cumulative frequency table for the given data: Age Frequency Cumulative Frequency 0 ≤ x < 10 1 1 10 ≤ x < 20 3 4 20 ≤ x < 30 8 12 30 ≤ x < 40 7 19 40 ≤ x < 50 7 26 50 ≤ x < 60 1 27 60 ≤ x < 70 3 30 A curve that represents the cumulative frequency distribution of grouped data on a graph is called a Cumulative Frequency Curve or an Ogive Steps to draw cumulative frequency curve: (i) Draw and mark the horizontal and vertical axes. (ii) Take the cumulative frequencies along the y -axis (vertical axis) and the end points of the class limit on the x -axis (horizontal axis). (iii) Against each end points of the class limit, plot the cumulative frequencies. (iv) Connect the points with a continuous curve. Cumulative frequency curve of the given data is,

Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise

Attempt the practice questions on Chapter 13: Statistics, Exercise 1: Exercise with hints and solutions to strengthen your understanding. Mathematics Crash Course (Based on Revised Syllabus-2023) solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise with Hints & Solutions

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10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 11

The number of books in different shelves of a library are as follows:

$\begin{array}{l} 30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20 \\ 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, \\ 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25 \end{array} \begin{array}{l} 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23 \\ 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21 \end{array}$

Prepare a cumulative frequency distribution table using $45 - 49$ as the last class interval.

HARD

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 12

In the following grouped frequency distribution table class marks are given:

Class marks	$10$	$22$	$34$	$46$	$58$	$70$
Frequency	$6$	$14$	$20$	$21$	$9$	$5$

Construct less than cumulative frequencies.

EASY

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 13

Define: class-boundary, lower and upper class-boundaries

MEDIUM

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 14

The weights (in $Kg$ ) of $20$ students of Barasat Gandhi Memorial High School are given below:

$\begin{matrix} 44 \\ 42 \end{matrix} \begin{matrix} 30 & 38 & 32 \\ 44 & 32 & 30 \end{matrix} \begin{matrix} 34 & 40 & 42 \\ 44 & 42 & 49 \end{matrix} \begin{matrix} 44 & 47 & 49 \\ 45 & 35 & 48 \end{matrix}$

Prepare a grouped frequency distribution table (with less than type cumulative frequency distribution) by taking the class-intervals $30 - 35, 35 - 40, . . . . . .$ etc. using tally-marks.

EASY

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 15

The height of students in a class is given below:

Create a frequency distribution table with class interval of $5 cm$

$150, 151, 152, 155, 164, 166, 155, 156, 151, 151, 157, 159, 161, 168, 169, 162, 163, 157, 154,$

EASY

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 20

Yield of coconuts grown in a village by 15 farmers is as follows. Draw less than type ogive.

Number of coconuts	Cumulative frequency
Less than $50$	$2$
Less than $75$	$4$
Less than $100$	$9$
Less than $125$	$10$
Less than $150$	$11$
Less than $175$	$13$
Less than $200$	$15$

EASY

10th Karnataka State Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 42

The following graph illustrates the times taken by $112$ people to complete a puzzle.

Question Image

The median is used to divide these people into two groups. Find the median time taken by each of the groups.

EASY

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 43

The ages (in years) of the first $30$ people visiting the Gardens in Paris on a certain day are shown.

$\begin{array}{l} 25 & 65 & 34 & 48 & 4 & 55 \\ 32 & 45 & 23 & 43 & 23 & 37 \\ 45 & 36 & 26 & 39 & 42 & 45 \\ 29 & 15 & 15 & 20 & 64 & 37 \\ 61 & 25 & 17 & 23 & 45 & 36 \end{array}$

Construct a cumulative frequency curve.

Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise

Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise

Questions from Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise with Hints & Solutions

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