Length (in mm)
No. of leaves
118-126
3
127-135
5
136-144
9
145-153
12
154-162
5
163-171
4
172-180
2
The length of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves

146.75 mm

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186.75 mm

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170.05 mm

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169.75 mm

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Solution

The correct option is A 146.75 mm
$C h a n g i n g t o c o n t i n u o s d o m a i n (s u b t r a c t i n g 0.5 f r o m l o w e r r a n g e a n d a d d i n g 0.5 t o t h e$
$u p p e r r a n g e a s 1 / 2 = 0.5)$

Length No of leaves Cum Freq

117.5 to 126.5 3 3

126.5 to 135.5 5 8

135.5 to 144.5 9 17

144.5 to 153.5 12 29

153.5 to 162.5 5 34

162.5 to 171.5 4 38

171.5 to 180.5
2 40

$N o w w e g e t a c o n t i n u o u s d o m a i n d a t a m a p N e x t, w e f i n d t h e c u m u l a t i v e f r e q v a l u e s i n t h e c o n t i n u o u s d o m a i n . W e f i n d t h e m e d i a n w i l l l i e h a l f o f 40 i e b e t w e e n 144.5 t o 153.5 r a n g e . A s w e k n o w t h e v a l u e o f m e d i a n o f c o n t i n u o u s d o m a i n = L + ((N / 2 - C) / f) * H H e r e L = 144.5, f = 12, C = 17, H = 9, N = 40 M e d i a n = 144.5 + ((20 - 17) / 12) * 9 = 146.75 T h e r e f o r e t h e m e d i a n i s = 146.75 m m$

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Similar questions

Q. The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table :

Lengths (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

Draw a histogram to represent the given data.

Q. The length of

40

leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table :

Length (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

Is there any other suitable graphical representation for the same data?

Q. The lengths of

40

leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:

Length (in mm)	118-126	127-135	136-144	145-153	154-162	163-171	172-180
No. of leaves:	$3$	$5$	$9$	$12$	$5$	$4$	$2$

Find the mean length of leaf.

The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table.

$\begin{matrix} Length (in mm) & Number of leaves 118 - 126 & 3 127 - 135 & 5 136 - 144 & 9 145 - 153 & 12 154 - 162 & 5 163 - 171 & 4 172 - 180 & 2 \end{matrix}$

Find the median length of leaves.

Question 4 (iii)
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:
$\begin{matrix} Length (in mm) & Number of leaves 118 - 126 & 3 127 - 135 & 5 136 - 144 & 9 145 - 153 & 12 154 - 162 & 5 163 - 171 & 4 172 - 180 & 2 \end{matrix}$
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

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Length (in mm)	No. of leaves
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-171	4
172-180	2

Length	No of leaves	Cum Freq
117.5 to 126.5	3	3
126.5 to 135.5	5	8
135.5 to 144.5	9	17
144.5 to 153.5	12	29
153.5 to 162.5	5	34
162.5 to 171.5	4	38
171.5 to 180.5	2	40

Length (in mm)No. of leaves118-1263127-1355136-1449145-15312154-1625163-1714172-1802The length of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves

Length (in mm)
No. of leaves
118-126
3
127-135
5
136-144
9
145-153
12
154-162
5
163-171
4
172-180
2
The length of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves