Question

The following data give the weekly amounts spent on groceries for a sample of 45 households.

$271	$363	$159	$76	$227	$337	$295	$319	$250
279	205	279	266	199	177	162	232	303
192	181	321	309	246	278	50	41	335
116	100	151	240	474	297	170	188	320
429	294	570	342	279	235	434	123	325

g. What percentage of the sales is within + one standard deviation

h. Explain the results of this analysis

Answer 1

First we copy paste this data set into excel.

This looks as follows:

Then for this data, we find the descriptive statistics by first typing all data values in a single column, as shown below:

The average value, called the mean, is equal to 254.2

The standard deviation is calculated using the formula STDEV.S as shown below:

The sample standard deviation in this case is:

S = 107.12

For range of within one standard deviation, we have:

Lower extreme value = 254.2-107.12 = 147.08

Upper extreme value = 254.2+107.12 = 361.32

Next we arrange this data in ascending order and count the number of values that fall within this range.

As we can see we have 34 values within this range.

So, % of values within 1 SD = (34/45)*100 = 75.56 %

This shows that most of the data values lie within one standard deviation from the mean, so the distribution is crowded near the mean.