Practice Pakistan questions with answers and explanations.
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Permutations count ordered arrangements.
Changing the order produces a different arrangement.
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Standard deviation is the square root of variance.
The square root of 25 is 5.
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Subtract the mean and divide by the standard deviation.
The z-score is (70 - 50) ÷ 10 = 2.
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Use x = mean + z × standard deviation.
Thus x = 80 + (-2)(5) = 70.
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Coefficient of variation is SD divided by mean times 100 percent.
CV = 8 ÷ 40 × 100% = 20%.
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The value 3 occurs three times, more than any other value.
Therefore, 3 is the mode.
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Adding a constant to every value adds the same constant to the mean.
Measures of spread such as standard deviation remain unchanged.
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The maximum is 25 and the minimum is 7.
The range is 25 - 7 = 18.
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Multiply each score by its weight and add the results.
The weighted mean is 80(0.40) + 70(0.60) = 74.
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Mean equals total divided by number of values.
Thus total = 12 × 5 = 60.
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Divide the total by the number of observations.
The mean is 144 ÷ 8 = 18.
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A mean of 10 for four values requires a total of 40.
The known values total 28, so x = 40 - 28 = 12.
