Question
Download Solution PDFThe weights (in g) of packets received in a post office in one day are given below. If the modal weight of the packets is 31.6 g, then what is the value of x?
| Weight (in g) | 16-22 | 22-28 | 28-34 | 33-40 | 40-46 |
| Number of packets | 13 | 16 | 25 | x | 20 |
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Modal weight = 31.6 g
Formula used:
Mode = L + [(fm - f1) ÷ (2fm - f1 - f2)] × h
Where,
L = Lower boundary of modal class = 28
fm = Frequency of modal class = 25
f1 = Frequency of class before modal class = 16
f2 = Frequency of class after modal class = x
h = Class width = 6
Calculation:
31.6 = 28 + [(25 - 16) ÷ (2 × 25 - 16 - x)] × 6
⇒ 31.6 - 28 = (9 ÷ (50 - 16 - x)) × 6
⇒ 3.6 = 54 ÷ (34 - x)
⇒ 3.6 × (34 - x) = 54
⇒ 122.4 - 3.6x = 54
⇒ 68.4 = 3.6x
⇒ x = 19
∴ The correct answer is 19.
Last updated on Apr 24, 2025
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