Question

Section 4.4

a) Go to problem 2.2.1 in the book

b) Calculate sample mean and sample standard deviation for the data;

c) Calculate x ̅-s,( x) ̅+s,x ̅-2s,( x) ̅+2s,x ̅-3s,( x) ̅+3s for the data;

d) Calculate the percentage of data points in (x ̅-s,( x) ̅+s), (x ̅-2s,( x) ̅+2s) and (x ̅-3s,( x) ̅+3s);

e) Check how these percentages compare with the suggested percentages in the empirical rule;

f) Give your comments on assessment of normality for the data.

Reference: Exercise 2.2.1

A paleontologist measured the width (in mm) of the last upper molar in 36 specimens of the extinct mammal Acropithecus rigidus. The results were as follows:

6.1 5.7 6.0 6.5 6.0 5.7

6.1 5.8 5.9 6.1 6.2 6.0

6.3 6.2 6.1 6.2 6.0 5.7

6.2 5.8 5.7 6.3 6.2 5.7

6.2 6.1 5.9 6.5 5.4 6.7

5.9 6.1 5.9 5.9 6.1 6.1

a) Construct a frequency distribution and display it as a table and as a histogram.

b) Describe the shape of the distribution.

Answer 1

mean	6.036
sample standard deviation	0.261
sample variance	0.068
empirical rule
mean - 1s	5.775
mean + 1s	6.297
percent in interval (68.26%)	69.4%
mean - 2s	5.514
mean + 2s	6.558
percent in interval (95.44%)	94.4%
mean - 3s	5.253
mean + 3s	6.819
percent in interval (99.73%)	100.0%

The data is approximately normally distributed.