1 For each of the following variables, identify the type of variable (numeric or categorical) and...

1 For each of the following variables, identify the type of variable (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 13.5 2.2 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 there any outliers in the data? Min: 13.2, Q1: 24.5, Med: 36, Q3: 42, Max: 53

Solutions

Expert Solution

a) business class ; type of variable = categorical

level of measurMent = ordinal

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

level of measurMent = ratio

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
total sum	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

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 NO OUTLIER

orchestra answered 1 year ago

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