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. (type an integer or decimal rounded to two decimal places as needed.) b. give the five - number summary and draw a boxplot for each of the two data sets. give the five number summary for the east coast counties. low value = lower quartile = median = upper quartile = high value = (type integers or decimals rounded to two decimal places as needed.) east coast counties a: 104.5, b: 128.9, c: 314.8, d: 134.8, e: 123.2, f: 141.2; midwest counties u: 96.3, v: 92.2, w: 94.9, x: 87.6, y: 95.5, z: 228.5

Explanation:

Step1: Order East Coast Data

First, we list the COLI values for East Coast counties: 104.5, 128.9, 314.8, 134.8, 123.2, 141.2. Sorting them in ascending order: 104.5, 123.2, 128.9, 134.8, 141.2, 314.8.

Step2: Find Low and High Values

The lowest value (minimum) is the first in the sorted list: 104.5. The highest value (maximum) is the last: 314.8.

Step3: Calculate Median (Q2)

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 the 3rd value is 128.9, 4th is 134.8. Median \( = \frac{128.9 + 134.8}{2} = \frac{263.7}{2} = 131.85 \).

Step4: Find Lower Quartile (Q1)

For the lower half (first 3 values: 104.5, 123.2, 128.9), \( n = 3 \) (odd), Q1 is the middle value: 123.2.

Step5: Find Upper Quartile (Q3)

For the upper half (last 3 values: 134.8, 141.2, 314.8), \( n = 3 \) (odd), Q3 is the middle value: 141.2.

Answer:

Low Value = 104.5
Lower Quartile = 123.2
Median = 131.85
Upper Quartile = 141.2
High Value = 314.8