Question

the table to the right gives the cost of living index (coli) for six east coast counties and six midwest counties (using an index where 100 represents the average cost of living for all participating cities with a population of more than 1.5 million). answer parts (a) through (e) below.
east coast counties | midwest counties
a | 104.5 | u | 96.3
b | 128.9 | v | 92.2
c | 314.8 | w | 94.9
d | 134.8 | x | 87.6
e | 123.2 | y | 95.5
f | 141.2 | z | 228.5
the standard deviation for the midwest counties is 55.29. (type an integer or decimal rounded to two decimal places as needed.)
d. apply the range rule of thumb to estimate the standard deviation of each of the two data sets. how well does the rule work in each case? briefly discuss why it does or does not work well.
the standard deviation for the east coast counties is approximately \\(\square\\), using the range rule of thumb. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Find the range of East Coast Counties

First, identify the maximum and minimum values in the East Coast Counties data. The values are 104.5, 128.9, 314.8, 134.8, 123.2, 141.2.
Maximum value ($\max$) = 314.8, Minimum value ($\min$) = 104.5.
Range = $\max - \min = 314.8 - 104.5 = 210.3$.

Step2: Apply the range rule of thumb

The range rule of thumb states that the standard deviation ($s$) is approximately $\frac{\text{Range}}{4}$.
So, $s \approx \frac{210.3}{4} = 52.575$. Rounding to two decimal places, we get 52.58.

Answer:

52.58