BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding stimulus
Model Answer
(i) Median Class:
Cumulative frequencies: 8, 17, 27, 39, 48.
n = 48, n/2 = 24. The cumulative frequency just exceeding 24 is 27 (class 30–45).
Median class = 30–45
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(ii) Probability of calling an even number (first ball):
Even numbers from 1 to 75: 2, 4, 6, … 74 → 37 even numbers
Total balls = 75
$$P(\text{even}) = \frac{37}{75}$$
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(iii) Median:
Median class = 30–45, l = 30, f = 10, cf = 17, h = 15, n/2 = 24
$$\text{Median} = l + \frac{\frac{n}{2} - cf}{f} \times h = 30 + \frac{24 - 17}{10} \times 15$$
$$= 30 + \frac{7 \times 15}{10} = 30 + 10.5 = \mathbf{40.5}$$
Source: Statistics, Median of Grouped Data
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Explanation
- Part (i): Build the cumulative frequency table; the class where cumulative frequency first reaches or exceeds n/2 = 24 is the median class.
- Part (ii): Balls are 1–75; even numbers are 2, 4, …, 74 = 37 numbers. Total = 75. Many students mistakenly write 38 — remember 75 is odd so evens = 37.
- Part (iii): Apply the standard median formula. Carry cf of the class before the median class (17, not 27). This is a common error to avoid.