Question

Problem:

Obtain a random sample size n of at least 30 on a random variable of your choice. Plot the frequency histogram, and compute the mean, standard deviation, and skew. Use the relative frequency histogram to determine the interval probability, cumulative probability, and exceedence probability of values of your choice (choose any valuss of your choice) Use the handout, in photos below, which contains precipitation data for College Station to guide you.

Illustrative example:(Ref. exampl The values of annual precipitation,x in College Station, Texas, from 1911 to 1979 given in Table 11.1.1 are presented in a data matrix below. Using Mathcad, plot the frequency histogram, compute the sample mean, sample standard deviation, and the sample coefficient of skewness. What is the probabililty that the annual precipitation R in any year will be less than 35 in? Greater than 45 in? Between 35 and 45 in? from Chow ORIGIN = 0 39.9 31.0 42.3 42.1 41.1 28.7 16.8 34.1 56.4 48.7 44.1 A-= 42.8 48.4 34.2 32.4 46.4 38.9 37.3 50.6 44.8 34.0 45.6 37.3 56.5 43.4 41.3 46.0 44.3 37.8 29.6 35.1 49.7 36.6 32.5 := | 61.7 47.4 33.9 31.7 43.7 41.1 31.2 35.2 35.1 49.3 44.2 41.7 30.8 53.6 B := | 34.5 | x := stack(A, B,C) 50.3 43.8 21.6 47.1 27.0 37.0 46.8 26.9 25.4 23.0 59.6 50.5 38.6 43.4 28.7 32.0 51.8

Answer 1

Let the random variable be marks obtained by 32 students of a class in Statistics subject for a maximum of 100 marks:

Here is the data set of marks obtained by 32 students:

47,48,50,52,53,55,58,58,

58,60,61,62,63,65,65,66,

69,69,70,70, 70,72,75,76,

77,77,79,85,85,89,90,93

Here is the frequency histogram of the above data:

Mean =67.72; Std.deviation =12.52; Skew or Skewness =0.28 (since skewness is positive, the data is skewed to the right).

Relative frequency and Cumulative relative frequency table:

Relative frequency histogram:

Probabilities:

Let P= Probability; X =score (marks)

Interval probability: P(71$\leq$X$\leq$78) =0.15625 and P(87$\leq$X$\leq$94) =0.09375

Cumulative probability: P(X $\leq$78) =0.8125 and P(X$\leq$94) =1

Exceedence probability: P(X>78) =1 - P(X$\leq$78) =1 - 0.8125 =0.1875 and P(X>94) =1 - P(X$\leq$94) =1 - 1 =0

(from relative frequency and cumulative relative frequency table).