Question

A students noted the number of cars pass through a spot on a road for 100 periods each of 3 minute and summarized 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

Answer 1

SOLUTION :  

FREQUENCY DISTRIBUTION TABLE is in the attachment

For MODE :  

Here the maximum frequency is 20, and the class corresponding to this frequency is 40 – 50. So the modal class is 40 – 50.

Therefore,l = 40 , h = 10,  f1= 20,  f0= 12 , f2 = 11

Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h

= 40 + [(20 - 12)/(2 × 20 - 12 – 11) ] ×10

= 40 + [8/ (40 - 23)]×10

= 40 + [(8×10)/17]

= 40 + [80/17]

= 40 + 4.7

= 44.7  

MODE = 44.7

Hence, the mode of the data is 44.7 .

★★ Mode = l + (f1-f0/2f1-f0-f2) ×h

l = lower limit of the modal class

h = size of the class intervals

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeed in the modal class.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

✔️✔️Refer the attachment ⬆️⬆️