Represent the following data by frequency polygon: Marks 10-20 20-30 30-40 40-50 50-60 Frequency 10 25 12 08 05

Given, Marks 10-20 20-30 30-40 40-50 50-60 Frequency 10 25 12 08 05 To draw the polygon we will first represent the class marks(i.e. mid point of class intervals) x 1 , x 2 , x 3 . . . x n along X -axis, and the frequencies along Y -axis. class mark = upper limit + lower limit 2 class mark = 10 + 20 2 , 20 + 30 2 , 30 + 40 2 , 40 + 50 2 , 50 + 60 2 = 15 , 25 , 35 , 45 , 55 Putting the points ( 15 , 10 ) , ( 25 , 25 ) , ( 35 , 12 ) , ( 45 , 08 ) , ( 55 , 05 ) and then joining them by straight lines we will get polygon. To find the last points we can take hypothetical class intervals as ( 0 - 10 ) , ( 60 - 70 ) one at the beginning and one at the ending. We will get ( 5 , 0 ) , ( 15 , 10 ) , ( 25 , 25 ) , ( 35 , 12 ) , ( 45 , 08 ) , ( 55 , 05 ) , ( 65 , 0 )

Represent the following data by frequency polygon. Class 0-10 10-20 20-30 30-40 40-50 Frequency 3 7 6 2 5

Given, Marks 0-10 10-20 20-30 30-40 40-50 Frequency 3 7 6 2 5 To draw the polygon we will first represent the class marks(i.e. midpoint of class intervals) x 1 , x 2 , x 3 . . . x n along the X-axis, and the frequencies along Y-axis. class mark = upper limit + lower limit 2 class mark = 0 + 10 2 , 10 + 20 2 , 20 + 30 2 , 30 + 40 2 , 40 + 50 2 = 5 , 15 , 25 , 35 , 45 Putting the points ( 5 , 3 ) , ( 15 , 7 ) , ( 25 , 6 ) , ( 35 , 2 ) , ( 45 , 5 ) and then joining them by straight lines we will get polygon. To find the last points we can take hypothetical class intervals as ( - 10 - 0 ) , ( 50 - 60 ) one at the beginning and one at the ending. We will get ( - 5 , 0 ) , ( 5 , 3 ) , ( 15 , 7 ) , ( 25 , 6 ) , ( 35 , 2 ) , ( 45 , 5 ) , ( 55 , 0 )

Represent the following data by frequency polygon. Class 20-29 30-39 40-49 50-59 60-69 Frequency 7 3 5 2 5

Given, Marks 20-29 30-39 40-49 50-59 60-69 Frequency 7 3 5 2 5 To draw the polygon we will first represent the class marks(i.e. midpoint of class intervals) x 1 , x 2 , x 3 . . . x n along the X -axis and the frequencies along Y -axis. class mark = upper limit + lower limit 2 class mark = 20 + 29 2 , 30 + 39 2 , 40 + 49 2 , 50 + 59 2 , 60 + 69 2 = 24 . 5 , 34 . 5 , 44 . 5 , 54 . 5 , 64 . 5 Putting the points ( 24 . 5 , 7 ) , ( 34 . 5 , 3 ) , ( 44 . 5 , 5 ) , ( 54 . 5 , 2 ) , ( 64 . 5 , 5 ) and then joining them by straight lines we will get polygon. To find the last points we can take hypothetical class intervals as ( 10 - 19 ) , ( 70 - 79 ) one at the beginning and one at the ending. We will get ( 14 . 5 , 0 ) , ( 24 . 5 , 7 ) , ( 34 . 5 , 3 ) , ( 44 . 5 , 5 ) , ( 54 . 5 , 2 ) , ( 64 . 5 , 5 ) , ( 74 . 5 , 0 )

Rohit asked people to draw a line 5 cm long using a straight edge without any markings on it, here are the lengths in centimetres of the line drawn 4.3 3.2 3.9 4.7 5.8 6.1 5.7 6.2 6.5 3.7 4.2 5.1 6.5 7.2 7.4 3.7 5.8 4.2 4.1 5.0 5.1 4.7 3.2 3.5 5.2 2.9 2.8 4.3 5.1 4.8 Draw frequency polygon for the data.

From the data we have formed the frequency distribution table as follows: lengths(cm) Frequency 2-3 2 3-4 6 4-5 8 5-6 8 6-7 4 7-8 2 To draw the polygon we will first represent the class line lengths(i.e. midpoint of class intervals) x 1 , x 2 , x 3 . . . x n along the X-axis,and the frequencies along Y-axis. class line length = upper limit + lower limit 2 ⇒ = 2 + 3 2 , 3 + 4 2 , 4 + 5 2 , 5 + 6 2 , 6 + 7 2 , 7 + 8 2 = 2 . 5 , 3 . 5 , 4 . 5 , 5 . 5 , 6 . 5 , 7 . 5 Putting the points ( 2 . 5 , 2 ) , ( 3 . 5 , 6 ) , ( 4 . 5 , 8 ) , ( 5 . 5 , 8 ) , ( 6 . 5 , 4 ) , ( 7 . 5 , 2 ) and the joining them by straight lines we will get polygon. To find the last points we can take hypothetical class intervals as ( 1 - 2 ) , ( 8 - 9 ) one at the beginning and one at the ending. We will get ( 1 . 5 , 0 ) , ( 2 . 5 , 2 ) , ( 3 . 5 , 6 ) , ( 4 . 5 , 8 ) , ( 5 . 5 , 8 ) , ( 6 . 5 , 4 ) , ( 7 . 5 , 2 ) , ( 8 . 5 , 0 )

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9th ICSE

IMPORTANT

Earn 100

Calculate the median from the following data,

Roll no $1$ $2$ $3$ $4$ $5$ $6$ $7$

Marks $25$ $55$ $5$ $45$ $15$ $35$ $60$

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Important Questions on Mean, Median and Frequency Polygon

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9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 8

Out of a total of $16$ observations arranged in ascending order, the $8^{th}$ and $9^{th}$ observations are $25$ and $27$ respectively. What is the median?

MEDIUM

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 9

The median of following observations arranged in ascending order,

$8, 9, 12, 18, (x + 2), (x + 4), 30, 31, 34, 39 is 24$ . What is $x$ ?

HARD

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 10

The following data have been arranged in ascending order:

$18, 20, 25, 26, 30, x, 37, 38, 39, 48$ .

If the median of the data is $35$ , find $x$ .

If $48$ is replaced by $28$ , find the new median.

HARD

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 1

Represent the following data by frequency polygon:

Marks	10-20	20-30	30-40	40-50	50-60
Frequency	10	25	12	08	05

HARD

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 2

Represent the following data by frequency polygon.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	3	7	6	2	5

MEDIUM

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 3

Represent the following data by frequency polygon.

Class	20-29	30-39	40-49	50-59	60-69
Frequency	7	3	5	2	5

MEDIUM

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 4

Rohit asked people to draw a line $5 cm$ long using a straight edge without any markings on it, here are the lengths in centimetres of the line drawn

Question Image

Draw up a grounded frequency table for the data. Use a class interval of $1 cm$ .

HARD

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 15 - Mean, Median and Frequency Polygon>Exercise>Q 4

Rohit asked people to draw a line $5 cm$ long using a straight edge without any markings on it, here are the lengths in centimetres of the line drawn

4.3	3.2	3.9	4.7	5.8	6.1
5.7	6.2	6.5	3.7	4.2	5.1
6.5	7.2	7.4	3.7	5.8	4.2
4.1	5.0	5.1	4.7	3.2	3.5
5.2	2.9	2.8	4.3	5.1	4.8

Draw frequency polygon for the data.

Roll no	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Marks	$25$	$55$	$5$	$45$	$15$	$35$	$60$

4.3	3.2	3.9	4.7	5.8	6.1
5.7	6.2	6.5	3.7	4.2	5.1
6.5	7.2	7.4	3.7	5.8	4.2
4.1	5.0	5.1	4.7	3.2	3.5
5.2	2.9	2.8	4.3	5.1	4.8

4.3	3.2	3.9	4.7	5.8	6.1
5.7	6.2	6.5	3.7	4.2	5.1
6.5	7.2	7.4	3.7	5.8	4.2
4.1	5.0	5.1	4.7	3.2	3.5
5.2	2.9	2.8	4.3	5.1	4.8

Calculate the median from the following data, Roll no 1 2 3 4 5 6 7 Marks 25 55 5 45 15 35 60

Important Questions on Mean, Median and Frequency Polygon

Learn and Prepare for any exam you want !

Calculate the median from the following data,

Roll no $1$ $2$ $3$ $4$ $5$ $6$ $7$

Marks $25$ $55$ $5$ $45$ $15$ $35$ $60$

4.3	3.2	3.9	4.7	5.8	6.1
5.7	6.2	6.5	3.7	4.2	5.1
6.5	7.2	7.4	3.7	5.8	4.2
4.1	5.0	5.1	4.7	3.2	3.5
5.2	2.9	2.8	4.3	5.1	4.8