Question

Consider a sample with 10 observations of –5, 10, 1, 2, 2, 1, 7, –5, 13, and 12. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

Find:

Z-score for the smallest observation -

Z-score for the largest observation -

There are ______ in the data -

Answer 1

From the given data, the following statistics are calculated:

n = Sample Size = 10

= Sample Mean = 38/10 = 3.8

s = Sample SD =6.4773

(i)

Smallest observation is given by:
X = - 5

So,

Z score for smallest observation is given by:

Z = (X - )/s

   = ( - 5 - 3.8)/6.4773 = - 8.8/6.4773 = - 1.36

So,

Since the absolute of of Z is less the 2, the smallest observation X = - 5 is not an outlier.

(ii)

Largest observation is given by:
X = 13

So,

Z score for largest observation is given by:

Z = (X - )/s

   = (13 - 3.8)/6.4773 = 9.2/6.4773 = 1.42

So,

Since the absolute of of Z is less the 2, the largest observation X = 13 is not an outlier.

So,

Z score for the smallest observation = - 1.36

Z score for the largest observation = 1.42

There are no outliers in the data.