Question

Q 14

Question 14

Consider the following sample of 11 length-of-stay values (measured in days):

1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8

Now suppose that due to new technology you are able to reduce the length of stay at your hospital to a fraction 0.3 of the original values. Thus, your new sample is given by

.3, .3, .6, .6, .6, .9, 1.2, 1.5, 1.8, 2.1, 2.4

Given that the standard deviation in the original sample was 2.5, in the new sample the standard deviation is _._. (Truncate after the first decimal.)

Answer 1

Solution:

We are given 11 values of length-of-stay measured in days and corresponding sample standard deviation = s= 2.5

New values are obtained by fraction of 0.3 of each values.

We have to find new sample standard deviation.

We use property of standard deviation;

Let y = Ax

then SD(y) = A * SD(x)

Let y be the new variable and x be the original variable and A = 0.3, then

SD(y) = A * SD(x)

SD(y) = 0.3 * 2.5

SD(y) = 0.75

SD(y) = 0.7        ( We have to truncate after first decimal)

Thus new sample standard deviation = 0.7