At Eurelia University the only marks given are A, B, C, D, and F. The letter gra

Question

At Eurelia University the only marks given are A, B, C, D, and F. The letter grades are converted for the purposes of calculating grade-point averages with A being given the value 4, B the value 3, C the value 2, D the value 1, and F the value 0. In a random sample of grades from statistics classes there were 17 As, 28 Bs, 10 Cs, 2 Ds, and 3 Fs. 1. Determine whether the F's are outliers by i) the boxplot criterion il) the z-score criterion. a) b) Which way are the data skewed? What percentage of the passing grades were A's? For the set of numerical equivalents, namely the sixty 4s, 3s, 2s, 1s, c) d) and Os, give a suitable sixtieth percentile.

Explanation / Answer

Answer:

a).

Q1=2.25

Q3=3

Q3=4

IQR = 4-2=1.75

Lower value for outlier = Q1-1.5*IQR = 2.25-1.5*1.75= -0.375

upper value for outlier = Q3+1.5*IQR = 3+1.5*1.75= 5.625

There is no outliers buy box plot criterion.

n

60

mean

2.90

sample standard deviation

1.0201

Z value for 4, z=(4-2.9)/1.0201 =1.08

Z value for 0, z=(0-2.9)/1.0201 =-2.84

0 is an outlier by z score criterion.

b).

data were negatively skewed.

c).

percentage = (17/60)*100 =28.33%

d).

60th percentile = (60*60)/100 = 36 th value in the ordered data

The 60th percentile = 3

n

60

mean

2.90

sample standard deviation

1.0201

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