To calculate the missing frequencies, we need to use the formula for the mean:
Mean = (Sum of (Frequency * Value)) / Total Frequency
In this case, the values are the number of accidents (0, 1, 2, 3, 4, 5) and the frequencies are the number of days for each value. The total frequency is given as 200.
We can set up the equation as follows:
1.46 = (0 * 46 + 1 * x + 2 * y + 3 * 25 + 4 * 10 + 5 * 5) / 200
Simplifying the equation:
1.46 = (x + 2y + 75 + 40 + 25) / 200
1.46 = (x + 2y + 140) / 200
Multiplying both sides by 200:
292 = x + 2y + 140
Subtracting 140 from both sides:
152 = x + 2y
Now we have one equation with two variables. We need another equation to solve for both x and y.
Since the total frequency is given as 200, we can set up another equation:
46 + x + y + 25 + 10 + 5 = 200
Simplifying the equation:
x + y + 86 = 200
Subtracting 86 from both sides:
x + y = 114
Now we have a system of equations:
152 = x + 2y x + y = 114
We can solve this system of equations using substitution or elimination method to find the values of x and y, which represent the missing frequencies.
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