Weight of students in a class is given below. Find the median of the data
Weight:
More than or less than 54
More than or less than 52
" " " " " 50
" " " " " 48
" " " " " 46
" " " " " 44
" " " " " 42
" " " " " 40
Number of students
0
3
5
9
14
28
32
35
Answers
U
10th
Maths
Statistics
Ogives
During the medical check - ...
STATISTICS
During the medical check-up of 35 students of a class, their weights were recorded as follows:
Weight (in kg)
Number of students
Less than 38
Less than 40
Less than 42
Less than 44
Less than 46
Less than 48
Less than 50
Less than 52
0
3
5
9
14
28
32
35
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
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VIDEO EXPLANATION
ANSWER
Let us now plot the points corresponding to the ordered pairs given by (38,0),(40,3),(42,5),(44,9),(46,14),(48,28),(50,32) and (52,35) on a graph paper and join them by a free hand smooth curve.
Now,
Weight (in kg) Number of students (Frequency)
0−38 0
38−40 3−0=3
40−42 5−3=2
42−44 9−5=4
44−46 14−9=5
46−48 28−14=14
48−50 32−28=4
50−52 35−32=3
Mode: The class which have highest frequency.
In this case, class interval 46−48 is the modal class.
Now,
Lower limit of modal class, l=46,h=2,f
1
,=14,f
0
=5,f
2
=4
We know that,
Mode =l+(
2f
1
−f
0
−f
2
f
1
−f
0
)×h=46+(
2(14)−5−4
14−5
)×2
=46+
19
9
×2
=46+0.95
Mode =46.95, verified.