Question

Given a sample of size 30: 7.34 8.16 8.69 8.80 8.82 9.28 9.29 9.38 9.43 9.51 9.65 9.78 9.84 9.95 9.98 9.99 10.02 10.05 10.37 10.42 10.52 10.67 10.78 10.87 11.05 11.12 11.19 11.37 11.54 11.92 to estimate the 1st quartile (25% point) from a distribution. Use binomial, how to find n and p value?

Answer 1

After Sorting:

7.34, 8.16, 8.69, 8.80, 8.82, 9.28, 9.29, 9.38, 9.43, 9.51, 9.65, 9.78, 9.84, 9.95, 9.98, 9.99, 10.02, 10.05, 10.37, 10.42, 10.52, 10.67, 10.78, 10.87, 11.05, 11.12, 11.19, 11.37, 11.54, 11.92

Median: (9.98 + 9.99) /2 ( Average of 15th and 16th terms)

Median=9.985

Therefore, the lower half of the data is: {7.34, 8.16, 8.69, 8.80, 8.82, 9.28, 9.29, 9.38, 9.43, 9.51, 9.65, 9.78, 9.84, 9.95, 9.98}

Then Q₁ = 9.38 (there are fifteen values in the lower half, so the middle value is the median).