Question

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes 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

The mode of the given data is 44.7

Number of cars:     Frequency  (fi)

0-10                                7

10-20                              14

20-30                              13

30-40                              12       f_0

40-50                              20       f_1

50-60                              11         f_2

60-70                              15

70-80                              8

The interval with the highest frequency is Modal class = 40 - 50

We use a formula to calculate the mode,

$Mode = l + \dfrac{f_1-f_0}{2f_1-f_0-f_2} * h$

where,

l = lower limit of modal class = 40

h = class interval = 10 - 0 = 20 - 10 = 10

f_1 = frequency of modal class = 20

f_0 = frequency of class before modal class = 12

f_2 = frequency of class after modal class = 11

$Mode = l + \dfrac{f_1-f_0}{2f_1-f_0-f_2} * h$

Mode = 40 + { (20-12) / [ 2×20 - 12 - 11]  } × 10

= 40 + 8/17 × 10

= 40 + 80/17

= 40 + 4.7

= 44.7

Answer 2

ㅤModal class = 40 - 50

ㅤL = 40

Class width ( h) = 10

ㅤ$f_1 = 20$

ㅤ$f_0 = 12$

ㅤ$f_2 = 11$

Mode = $\bf { L + \dfrac {f_1 - f_0}{2f_1 - f_0 - f_2} \times h}$

=${40 + \frac {20-12}{40-12-11}\times 10}$

=$40 + \frac{80}{17}$

= 40 + 4.7

= 44.7

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