Question

For our sample of student's measurements we expect that 68% of the values to fall within one σ (0.23mm) from our mean davg (21.00mm). Diameter, mm # of students 20.4 2 20.5 12 20.6 10 20.7 33 20.8 40 20.9 76 21.0 80 21.1 65 21.2 52 21.3 22 21.4 12 21.5 5 21.6 11 Using the data given above determine what percentage of the measurements fall within one standard deviation of the average.

Answer 1

Answer: 74.5% of the measurements fall within one standard deviation of the average.

Explanation:

The total number of measurements given is 2 + 12 + 10 + 33 + 40 + 76 + 80 + 65 + 52 + 22 + 12 + 5 + 11 = 420

If the mean is 21 mm and one standard deviation is 0.23 mm, then one standard deviation from the mean would be

21 ± 0.23

The lower limit is 20.77 mm

The upper limit is 21 + 0.23 = 21.23 mm

The number of measurements that fall within this range are

20.8 × 40

20.9 × 76

21.0 × 80

21.1 × 65

21.2 × 52

The total number of measurements that fall within this range is

40 + 76 + 80 + 65 + 52 = 313

The percentage of the measurements that fall within one standard deviation of the average is

313/420 × 100 = 74.5%