The length of 42 leaves of a plant are measure correct up to the nearest millimeter and the17:data is as under:Length (in m)118-126126-134134-142142-150150-158158-166Number ofleaves45101445Find the mode length of the leaves.
Answers
Answer:
63:67
Step-by-step explanation:
Answer:
146.75
Step-by-step explanation:
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)
Number of leaves
118−126 3
127−135 5
136−144 9
145−153 12
154−162 5
163−171 4
172−180 2
The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to (117.5−126.5,126.5−135.5,...,171.5−180.5.)
Converting the given table into exclusive form and preparing the cumulative frequency table, we get
We have, n=40
⇒
2
n
=20
The cumulative frequency just greater than
2
n
is 29 and the corresponding class is 144.5−153.5.
Thus, 144.5−153.5 is the median class such that
2
n
=20,l=144.5,cf=17,f=12, and h=9
Substituting these values in the formula
Median, M=l+
⎝
⎛
f
2
n
−cf
⎠
⎞
×h
M=144.5+(
12
20−17
)×9
M=144.5+
12
3
×3=144.5+2.25=146.75
Hence, median length =146.75