Answer:
a) Range = 25.6
b) Variance = 48.1446
c) s = 6.9386
d) See below
Step-by-step explanation:
(a) the sample range
To obtain the sample range, we must <em>sort the data increasingly</em>
:
23.7, 26.3, 28.3, 28.7, 29.6, 29.8, 30.1, 31, 33.5, 49.3
Then, find the <em>distance between the largest and the lowest
</em>
Range = 49.3 - 23.7 = 25.6
(b) the sample variance
from the definition
In order to find the variance from the definition, we need first the mean. The mean is defined as the average
where the
are the values of the data collected and <em>n=10</em> the size of the sample.
So, <em>the mean</em> is
Now, t<em>he variance of the sample </em>is defined as
and we have that <em>the variance</em> is
(c) the sample standard deviation
The sample standard deviation is nothing but the <em>square root of the variance
</em>
d)
using the shortcut method
The <em>shortcut method</em> figures out the variance without having to compute the mean. The formula is
where n=10 is the sample size
.
So, using the shortcut method,