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

CBSE Class 10 Maths PYQ · Statistics · Find Mean, median, mode · 5 Marks · March 2023 · Standard

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455 Marks · March 2023 · Standard

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 mean and median of the following data.
Number of cars
Frequency (periods)
0-10
7
10-20
14
20-30
13
30-40
12
40-50
20
50-60
11
60-70
15
70-80
8

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Correct table
Number of cars
$x_i$
f$_i$
$x_i f_i$
c.f.
0-10
5
7
35
7
10-20
15
14
210
21
20-30
25
13
325
34
30-40
35
12
420
46
40-50
45
20
900
66
50-60
55
11
605
77
60-70
65
15
975
92
70-80
75
8
600
100
Total
100
4070
Mean = $\frac{\Sigma x_i f_i}{\Sigma f_i} = \frac{4070}{100} = 40.7$
Median class : $40 – 50$
Median = $40 + \frac{50-46}{20} \times 10 = 42$