Find the mode of the following data:
Marks Below $10$ Below $20$ Below $30$ Below $40$ Below $50$
No. of Students 8 20 45 58 70

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Solution

Marks No. of students
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50 8
12 [20-8]
25 [45-20]
13 [58-45]
12 [70-58]
The group with $25$ students has highest frequency
Hence modal class $= 20 - 30$
Mode = $l + [\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}] \times h$
$l = 20, f_{1} = 25, f_{2} = 13, f_{0} = 12, h = 10$
$= 20 + [\frac{25 - 12}{50 - 12 - 13}] \times 10$
$= 20 + 5.2 = 25.2$

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Marks	No. of students
0 - 10 10 - 20 20 - 30 30 - 40 40 - 50	8 12 [20-8] 25 [45-20] 13 [58-45] 12 [70-58]

Find the mode of the following data:MarksBelow10Below20Below30Below40Below50No. of Students820455870

MarksNo. of students 0 - 1010 - 2020 - 3030 - 4040 - 50 812 [20-8]25 [45-20]13 [58-45]12 [70-58]The group with 25 students has highest frequencyHence modal class =20−30Mode = l+[f1−f02f1−f0−f2]×hl=20,f1=25,f2=13,f0=12,h=10=20+[25−1250−12−13]×10=20+5.2=25.2

Find the mode of the following data:
Marks Below $10$ Below $20$ Below $30$ Below $40$ Below $50$
No. of Students 8 20 45 58 70