Question

using technology to calculate measures of center
meteorologists look for weather trends across us states in the same geographical region. kentucky and illinois share a border. the average annual temperatures (°f) from 1991 to 2000 for kentucky were 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7. the average annual temperatures (°f) from 1991 to 2000 for illinois were 53.7, 51.9, 50.9, 51.8, 51.4, 49.9, 50.8, 55.0, 53.3, and 52.0. use the statistics calculator to determine the measures of center for kentucky.
kentucky mean =
illinois mean = 52.07
kentucky median =
illinois median = 51.85
both measures of center for kentucky are
those of illinois.

Explanation:

Step1: Calculate Kentucky mean

The data for Kentucky's average annual temperatures (°F) from 1991 to 2000 is: 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, 55.7.
First, sum all the values:
\[

$$\begin{align*} &57.5 + 55.1 + 52.2 + 55.6 + 55.6 + 54.4 + 54.5 + 58.3 + 57.3 + 55.7\\ =&(57.5 + 55.1)+(52.2 + 55.6)+(55.6 + 54.4)+(54.5 + 58.3)+(57.3 + 55.7)\\ =&112.6 + 107.8 + 110 + 112.8 + 113\\ =&112.6+107.8 = 220.4\\ &220.4+110 = 330.4\\ &330.4+112.8 = 443.2\\ &443.2+113 = 556.2 \end{align*}$$

\]
There are 10 data points, so the mean is the sum divided by 10:
\[
\text{Mean}=\frac{556.2}{10}=55.62
\]

Step2: Calculate Kentucky median

First, order the data set: 52.2, 54.4, 54.5, 55.1, 55.6, 55.6, 55.7, 57.3, 57.5, 58.3.
Since there are 10 (even number) data points, the median is the average of the 5th and 6th values.
The 5th value is 55.6 and the 6th value is 55.6.
\[
\text{Median}=\frac{55.6 + 55.6}{2}=\frac{111.2}{2}=55.6
\]

Step3: Compare with Illinois

Illinois mean = 52.07, Illinois median = 51.85.
Kentucky's mean (55.62) is greater than Illinois' mean (52.07), and Kentucky's median (55.6) is greater than Illinois' median (51.85). So both measures of center for Kentucky are greater than those of Illinois.

Answer:

Kentucky mean = 55.62; Kentucky median = 55.6; Both measures of center for Kentucky are greater than those of Illinois.