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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