Question

what is the population standard for the numbers 75, 83, 96, 100, 121 and 125?

Answer 1

Answer:

= 18.2 correct to 1 decimal places

Step-by-step explanation:

1. Firstly find the mean:

Mean = (75 + 83 + 96 + 100 + 121 + 125) ÷ 6 = 600 ÷ 6 = 100

2. Next find the variance. To calculate the Variance, take each difference, square it, and then average the result:

(75 - 100)2 + (83 - 100)2 + (96 - 100)2 + (100 - 100)2 + (121 - 100)2 + (125 - 100)2

= (-25)2 + (-17)2 + (-4)2 + (0)2 + (21)2 + (25)2

= 625 + 289 + 16 + 0 + 441 + 625

= 1,996

So the Variance = 1,996 ÷ 6 = 332.66...

3. The Standard Deviation is just the square root of the Variance

= √(332.66...)

= 18.2 correct to 1 decimal places

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