Question

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 1901 to 2000 for kentucky were 55.0, 54.4, 54.5, 58.3, 57.3, and 55.7. the average annual temperatures (°f) from 1901 to 2000 for illinois were 53.7, 51.9, 50.9, 51.0, 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 is \(57.5, 55.1, 52.2, 55.6, 53.7, 51.9, 60.9, 51.0, 51.4, 49.9, 50.8, 55.0, 53.3, 52.0\). Mean formula is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 14\) and \(\sum_{i=1}^{14}x_{i}=57.5 + 55.1+52.2+55.6+53.7+51.9+60.9+51.0+51.4+49.9+50.8+55.0+53.3+52.0 = 749.3\). So, \(\bar{x}=\frac{749.3}{14}\approx53.52\).

Step2: Calculate Kentucky median

Arrange the data in ascending - order: \(49.9, 50.8, 51.0, 51.4, 51.9, 52.0, 52.2, 53.3, 53.7, 55.0, 55.1, 55.6, 57.5, 60.9\). Since \(n = 14\) (even), median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}=\frac{52.2 + 53.3}{2}=52.75\).

Step3: Compare with Illinois values

Illinois mean is \(52.07\) and median is \(51.85\). Kentucky mean (\(53.52\)) and median (\(52.75\)) are greater than Illinois mean and median.

Answer:

Kentucky mean = \(53.52\)
Kentucky median = \(52.75\)
Both measures of center for Kentucky are greater than those of Illinois.