Question

It is known that the highest weekly average price for gasoline in California during 2005 was $3.15 per gallon and the lowest weekly average price for gasoline in California during 2005 was $2.56. Use this information to estimate the standard deviation of the weekly average price for gasoline in California during 2005. The standard deviation is ($3.15-2.56) / 6. I was wondering why you divide by 6?

Answer 1

Dividing the range of the weekly gas prices by 6 is a rough method of estimating standard deviation when data is not normally distributed, covering about 6 standard deviations.

Step-by-step explanation:

The question pertains to estimating the standard deviation of the weekly average price for gasoline in California during 2005. The information given was the highest and lowest weekly average prices, $3.15 and $2.56 respectively. To estimate the standard deviation, we use the range rule of thumb, which involves subtracting the lowest value from the highest (the range) and dividing by 4 to estimate the standard deviation if the data forms a bell-shaped distribution. However, dividing by 6 can be used for a rougher estimate if the data does not follow a normal distribution and assuming that the range covers about 6 standard deviations. This rule assumes that most data lie within +/- 3 standard deviations from the mean (which encompasses about 99.7% of the data if it is normally distributed).

Answer 2

$0.15

Step-by-step explanation:

To solve this problem, we apply the Range rule for estimating Standard deviation.

By the Range Rule:

Standard Deviation

Highest weekly average price for gasoline= $3.15 per gallon.

Lowest weekly average price for gasoline =$2.56 per gallon.

Therefore:

`\text{Standard Deviation}\approx (3.15-2.56)/(4) \\=(0.59)/(4) \\\\=\$0.15 $(correct to the nearest cent).`

The standard deviation of the weekly average price for gasoline is approximately $0.15.

NOTE: You divide by 4 not 6.