Draw an ogive to represent the following frequency distribution: Class-interval Number of students 0 - 4 2 5 - 9 6 10 - 14 10 15 - 19 5 20 - 24 3

The given frequency distribution is not continuous. So, we first make it continuous and prepare the cumulative frequency distribution as under: Class-interval Number of students Upper class limits Cumulative frequency 0 - 4 . 5 2 Less than 4 . 5 2 4 . 5 - 9 . 5 6 Less than 9 . 5 8 9 . 5 - 14 . 5 10 Less than 14 . 5 18 14 . 5 - 19 . 5 5 Less than 19 . 5 23 19 . 5 - 24 . 5 3 Less than 24 . 5 26 Now, we mark the upper class limits or upper boundaries along x -axis and cumulative frequencies along y -axis. Thus, we plot the points ( 4 . 5 , 2 ) , ( 9 . 5 , 8 ) , ( 14 . 5 , 18 ) , ( 19 . 5 , 23 ) and 24 . 5 , 26 .

The following table gives the height of trees: Height No. of trees Less than 7 26 Less than 14 57 Less than 21 92 Less than 28 134 Less than 35 216 Less than 42 287 Less than 49 341 Less than 56 360 Draw 'less than' ogive and 'more than' ogive.

Less than method : Height Cumulative frequency Less than 7 26 Less than 14 57 Less than 21 92 Less than 28 134 Less than 35 216 Less than 42 287 Less than 49 341 Less than 56 360 Now, we mark the upper class limits along x -axis and less than cumulative frequency along y -axis. Thus, we plot ( 7 , 26 ) , ( 14 , 57 ) , ( 21 , 92 ) , ( 28 , 134 ) , ( 35 , 216 ) , ( 42 , 287 ) , ( 49 , 341 ) & ( 56 , 360 ) . More than method : We prepare the cumulative frequency table by more than method as given below : Height Frequency Height Cumulative frequency 0 - 7 26 More than 0 360 7 - 14 31 More than 7 334 14 - 21 35 More than 14 303 21 - 28 42 More than 21 268 28 - 35 82 More than 28 226 35 - 42 71 More than 35 144 42 - 49 54 More than 42 73 49 - 56 19 More than 49 19 Now, we mark the lower class limits on x -axis and more than cumulative frequency along y -axis. Thus, we plot the ( 0 , 360 ) , ( 7 , 334 ) , ( 14 , 303 ) , ( 21 , 268 ) , ( 28 , 226 ) , ( 35 , 144 ) , ( 42 , 73 ) & ( 49 , 19 ) .

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,

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 35

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IMPORTANT

Earn 100

The length or class width of the class interval $26 - 30$ is , when class interval is inclusive or non-overlapping when gap is $1$ .

50% studentsanswered this correctly

Important Questions on Statistics

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 36

Construction of a cumulative frequency table is useful in determining the

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 37

What is the class-mark of class

25 - 35

?

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 38

The classmark of a class Interval is

MEDIUM

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 39

The median of a given frequency distribution is found graphically with the help of

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 40

Draw an ogive to represent the following frequency distribution:

Class-interval	Number of students
$0 - 4$	$2$
$5 - 9$	$6$
$10 - 14$	$10$
$15 - 19$	$5$
$20 - 24$	$3$

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IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 13 - Statistics>Exercise>Q 41

The following table gives the height of trees:

Height	No. of trees
Less than $7$	$26$
Less than $14$	$57$
Less than $21$	$92$
Less than $28$	$134$
Less than $35$	$216$
Less than $42$	$287$
Less than $49$	$341$
Less than $56$	$360$

Draw 'less than' ogive and 'more than' ogive.

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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.

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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.

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