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A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:
Number of cars: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Frequency: | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
To do:
We have to find the mean, median and mode of the above data.
Solution:
The frequency of the given data is as given below.
Number of cars ($x_i$): | Frequency ($f_i$): |
0-10 | 7 |
10-20 | 14 |
20-30 | 13 |
30-40 | 12 |
40-50 | 20 |
50-60 | 11 |
60-70 | 15 |
70-80 | 8 |
We observe that the class interval of 40-50 has the maximum frequency(20).
Therefore, it is the modal class.
Here,
$l=40, h=10, f=20, f_1=12, f_2=11$
We know that,
Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$
$=40+\frac{20-12}{2 \times 20-12-11} \times 10$
$=40+\frac{8}{40-23} \times 10$
$=40+\frac{80}{17}$
$=40+4.70$
$=44.7$
The mode of the given data is 44.7(cars).
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