calculate the mode of following distribution
Marks 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
number of students 29 87 181 247 263 133 40 9 2
Answers
Answer:
50-59. 263
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Given : Distribution of Marks of Students
To find : Mode of Distribution
Solution:
Marks 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
students 29 87 181 247 263 133 40 9 2
Class f cf
9.5 - 19.5 29 29
19.5 - 29.5 87 116
29.5 - 39.5 181 297
39.5 - 49.5 247 544
49.5 - 59.5 263 807
59.5 - 69.5 133 940
69.5 - 79.5 40 980
79.5 - 89.5 9 989
89.5 - 99.5 1 991
Maximum frequency 263 from 49.5 - 59.5
Mode = 49.5 + 10 * ( 263 - 247)/(263 - 247 + 263 - 133)
= 49.5 + 10 * 16 / 146
= 49.5 + 1.1
= 50.6
Mode = 50.6
Median will lie in 39.5 - 49.5
Median = 39.5 + 10 * ( 991/2 - 297)/247
= 39.5 + 8
= 47.5
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