The number of faulty items found in each of 30 batches inspected was: 0 faulty items: 6 batches 1 faulty item: 9 batches 2 faulty items: 10 batches 3 faulty items: 3 batches 4 faulty items: 2 batches Treating the 30 batches as the whole population, what is the standard deviation of the number of faulty items per batch (to two decimal places)?

Correct answer: A) 1.12

Explanation

Sum of f = 30. Sum of fx = 0 + 9 + 20 + 9 + 8 = 46, so mean = 46 / 30 = 1.5333. Sum of fx squared = 0 + 9 + 40 + 27 + 32 = 108, so sum of fx squared / sum of f = 3.6. Variance = 3.6 - 1.5333 squared = 3.6 - 2.3511 = 1.2489. Standard deviation = square root of 1.2489 = 1.12 (rounded to two decimal places). 1.25 is the variance, 1.90 is the square root of 3.6 (forgetting to subtract the squared mean) and 1.41 ignores the frequencies.