Let's start with a popular definition of an outlier.

A point, , that meets the following criteria:

Is not considered an outlier; any point outside this range is. In the preceding equation, Q¹ is the first quartile (25^th percentile), Q³ is the third quartile, and IQR is the interquartile range and is defined as the difference between Q³ and Q¹ : IQR= Q³-Q¹. 

To flag the outliers, follow these steps:

1. Let's calculate our ranges first:

features = ['Displacement', 'Cylinders', 'FuelEconomy']
quantiles = [0.25, 0.75]

cut_off_points = []

for feature in features:
    quants = imputed.approxQuantile(feature, quantiles, 0.05)
    
    IQR = quants[1] - quants[0]
    cut_off_points.append((feature, [
        quants[0] - 1.5 * IQR,
        quants[1] + 1.5 * IQR,
    ]))
    
cut_off_points = dict(cut_off_points)

2. Next, we flag the outliers:

outliers = imputed.select(*['id'] + [
       (
           (imputed[f] < cut_off_points[f][0]) |
           (imputed[f] > cut_off_points[f][1])
       ).alias(f + '_o') for f in features
  ])