Sample Variance Question

Question

Hi, I am reading a book for a hobby that has a math calculation I don't understand. I haven't been in school in 10 years.

The book reads: Now record the variation from the average of the seven samples, which is +2.572 and -4.428 weeks. Average these limits to obtain t3.5 weeks.

The sample included the numbers: 23,9,21,12,22,24,17

Can someone tell me how the limits were obtained and what type of calculators I could use to perform these calculations myself?

Thanks!

Answer 1

The Average or Mean of the sample equals (9 + 12 + 17 + 21 + 22 + 23 +24) ÷ 7 or 128/7.

Variance for the 7 Data Points in the sample is given by:

[(9 − 128/7)² + (12 − 128/7)² + (17 − 128/7)² + (21 − 128/7)² + (22 − 128/7)² + (23 − 128/7)² + (24 − 128/7)²] ÷ (7 − 1) which simplifies to 33.90476191.

Note that, if the given 7 Data Points were an entire population instead of a sample of an entire population, then the Variance would be given by:

[(9 − 128/7)² + (12 − 128/7)² + (17 − 128/7)² + (21 − 128/7)² + (22 − 128/7)² + (23 − 128/7)² + (24 − 128/7)²] ÷ (7 − 0) which simplifies to 29.06122449.