Home > INT3 > Chapter 1 > Lesson 1.2.2 > Problem1-88

1-88.

Because gathering data for entire populations is often impractical, most of the data sets we analyze are samples. In order to make the sample standard deviation more closely estimate the population standard deviation, statisticians modify the way they calculate the standard deviation for a sample. Refer to the Math Notes box in this lesson to learn how to calculate standard deviation for a sample.

A nonprofit consumer health organization measured the fat content of five low fat raspberry muffins purchased at random Sunbucks coffee shops to have $6, 8, 8, 9,$ and $7$ grams of fat. What are the mean and sample standard deviation of the amount of fat in one of these muffins?

Do the computations step by step, without using the “standard deviation” function on your calculator.

Find the mean.

mean $= 7.6$

Find the distances to the mean from each data point.

$6 - 7.6 = -1.6$
$8 - 7.6 = ?$
$8 - 7.6 = ?$
$9 - 7.6 = ?$
$7 - 7.6 = ?$

Square the distances.

$-1.6$ distance squared $= 2.56$
$.4$ distance squared $= .16$
$?$
$?$
$?$

Find the mean of the distances squared.
Since this is a sample, divide by one less than the number of data items.

$1.14$ g