Question
Download Solution PDFCalculate the mode of the following frequency distribution
|
Seconds |
51-55 |
56-60 |
61-65 |
66-70 |
|
Frequency |
2 |
7 |
8 |
4 |
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given,
|
Seconds |
Frequency |
|
51 – 55 |
2 |
|
56 - 60 |
7 |
|
61 – 65 |
8 |
|
66 - 70 |
4 |
The interval is not continuous, therefore subtract 0.5 from the lower limit and add 0.5 in the upper limit.
Now, the table will be
|
Seconds |
Frequency |
|
50.5 – 55.5 |
2 |
|
55.5 - 60.5 |
7 |
|
60.5 – 65.5 |
8 |
|
65.5 - 70.5 |
4 |
The interval with the highest frequency is 60.5 - 65.5.
Modal class = 60.5 – 65.5 ( Highest frequency = 8)
Formula
Mode = L +
I = class interval or class size = 5
f1 = frequency of modal class = 8
f0 = frequency of class preceding modal class = 7
f2 = frequency of class succeeding modal class = 4
L = lower limit of modal class = 60.5
Mode = 60.5 +
= 60.5 + [
= 60.5 +
= 60.5 + 1
∴ The mode is 61.5.
The correct answer is option (1).
Last updated on Jul 21, 2025
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