x = c(rep.int(11,2),rep.int(14,1),rep.int(17,2),rep.int(20,1),rep.int(23,6),rep.int(26,7),rep.int(29,11),rep.int(32,12),rep.int(35,12),rep.int(38,17),rep.int(41,19),rep.int(44,9),rep.int(47,0),rep.int(50,0),rep.int(53,1))

n = length(x);

print("min:");
print(min(x))

print("max:");
print(max(x))
 
print("mean:"); 
xbar = sum(x)/n
print(xbar);

xm = (x - xbar)^2

s2 = sum(xm)/(n-1)
s = sqrt(s2)

sigma2 = sum(xm)/n;
sigma = sqrt(sigma2)

print("sample variance:")
print(s2)

print("sample mean:")
print(s)

print("population variance:")
print(sigma2)

print("get class counts for frequency table");
sum(x >= 10 & x<=16.9)

sum(x >= 17 & x<=23.9)

sum(x >= 24 & x<=30.9)

sum(x >= 31 & x<=37.9)

sum(x >= 38 & x<=44.9)

sum(x >= 45 & x<=51.9)

sum(x >= 52 & x<=58.9)

printf("compute five number summary components");
sx = sort(x);

L25 = (25/100)*n; # check that it's a whole number
L50 = (50/100)*n;
L75 = (75/100)*n;

Q1 = (sx[L25] + sx[L25+1])/2

Q2 = (sx[L50] + sx[L50+1])/2

Q3 = (sx[L75] + sx[L75+1])/2

iqr = Q3 - Q1

lowoutlier = Q1 - 1.5*iqr

highoutlier = Q3 + 1.5*iqr

print("five number summary:")

print("how many outliers:")
sum(x < lowoutlier)
sum(x > highoutlier)

arr1 = c(xbar - s, xbar + s)

arr2 = c(xbar - 2*s, xbar + 2*s)

print("one and two std deviations from mean intervals:");

print(arr1)

print(arr2)

print("how percent many fall within one std deviation")
print(sum(x>=arr1[1] & x<=arr1[2])/n * 100)

print("how percent many fall within two std deviations")
print(sum(x>=arr2[1] & x<=arr2[2])/n * 100)

print("five number summary")
print("min,max:")
print(min(x))
print(max(x))
print("Q1,Q2,Q3:");
print(Q1)
print(Q2)
print(Q3)