Question

Problem 1. [40 pts] The annual peak discharge (in cubic feet per second) at a river location is available below: 2000 to 2009 7896 2302 18504 1884 1711 1802 5040 2393 4128 2904 2010 to 2019 2239 4392 4296 10968 7728 1834 19536 14064 10608 7176 (a) Compute the sample arithmetic, geometric, and harmonic means. (b) Compute the sample median. (c) Compute the sample mode. (d) Compute the sample standard deviation, variance, and coefficient of variation. (e) Compute the sample skewness and kurtosis coefficients. Is the sample left or right skewed? (1) Create time series plot, histogram, and boxplot of the data, (e) Create the empirical cumulative relative frequency plot of the data. (h) Using the empirical CDF, compute median (X.) and 0.99 quantile (X0.99) of the data using the quantile estimation procedure. (Ans.: Xm = 4344 cfs). (0) Using the empirical CDF, compute the probability that annual peak discharge at this location exceeds 10,000 cfs. (Ans.: 0.2488) 0) Can you compute the probability that annual peak discharge at this location is exactly 10,000 cfs ?

Answer 1

Coefficient of variation = - 15397-328 10o) = - 1570.25 - 82.147f. sample median - 4344 Sample mode = 1799 From data, 1884, 1711 & 1802 are most nearest data Hence, an average of them is taken as mode mode = 1884 +1714 1802 hence ² 1799