1 For each of the following va

1 For each of the following variables, identify the type ofvariable (numeric or categorical) and level of measurement(nominal, ordinal, interval, or ratio). a. Business size (micro,small, medium, large) b. Airplane ticket price

2 Consider the following sample of data: 1.2 28.4 32.6 17.0 13.52.2 38.0 41.4 1.9 14.4 21.8 23.8 a. Calculate the quartiles. b.Calculate the average c. Calculate the standard deviation.

3  Given the following ﬁve-number summary, are thereany outliers in the data? Min: 13.2, Q1: 24.5, Med: 36, Q3: 42,Max: 53

Answer:

1

a) business class ; type of variable = categorical

level of measurMent = ordinal

b) airplane ticket price: ; type of variable = numeric

level of measurMent = ratio

2)

 X (X – X̄)² 1.2 341.63 1.9 316.25 2.2 305.67 13.5 38.23 14.4 27.91 17 7.20 21.8 4.480 23.8 16.947 28.4 75.980 32.6 166.840 38 335.500 41.4 471.614
 X (X – X̄)² totalsum 236.2 2108.26 n 12 12

quartile , Q1 = 0.25(n+1)th value=  3.25th   value of sorted data=   5.025        Quartile , Q3 = 0.75(n+1)th value=   9.75th  value of sorted data=   31.55

mean =    ΣX/n =    236.200  /   12   =   19.6833

sample std dev =   √ [ Σ(X – X̄)²/(n-1)]=   √   (2108.2567/11)  =       13.844

3)

min = 13.2

Q1=24.5

Med = 36

Q3= 42

Max =53

IQR = Q3-Q1 = 42 – 24.5 =17.5

lower bound=Q1-1.5IQR= 24.5 – 1.5 * 17.5 = -1.75

UPPER BOUND = Q3 + 1.5 IQR = 42+ 1.5* 17.5 = 68.25

LIMITS (-1.75,68.25)

Min and max value fall in IQR limits so NOOUTLIER

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