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
...
give the five - number summary for the midwest counties.
low value =
lower quartile =
median =
upper quartile =
high value =
(type integers or decimals rounded to two decimal places as needed.)

Explanation:

Step1: Order the Midwest data

First, we list the COLI values for Midwest Counties: 96.3, 92.2, 94.9, 87.6, 95.5, 228.5. Then we sort them in ascending order: 87.6, 92.2, 94.9, 95.5, 96.3, 228.5.

Step2: Find Low Value

The lowest value in the sorted list is the first element. So Low Value = 87.6.

Step3: Find Median (for even number of data points)

For \( n = 6 \) (even), the median is the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th values. \( \frac{6}{2}=3 \), so we take the 3rd and 4th values: 94.9 and 95.5. Median \(=\frac{94.9 + 95.5}{2}=\frac{190.4}{2}=95.2\).

Step4: Find Lower Quartile (Q1)

The lower half of the data is the first 3 values: 87.6, 92.2, 94.9. The median of this lower half is the 2nd value (since \( n = 3 \), median is the middle value). So Q1 = 92.2.

Step5: Find Upper Quartile (Q3)

The upper half of the data is the last 3 values: 95.5, 96.3, 228.5. The median of this upper half is the 2nd value (since \( n = 3 \), median is the middle value). So Q3 = 96.3.

Step6: Find High Value

The highest value in the sorted list is the last element. So High Value = 228.5.

Answer:

Low Value = 87.6
Lower Quartile = 92.2
Median = 95.2
Upper Quartile = 96.3
High Value = 228.5