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 1991 to 2000 for kentucky were 57.5, 55.1, 52.2, 55.6, 55.0, 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. less than greater than equal to

Explanation:

Step1: Calculate Kentucky mean

Sum all Kentucky temperatures and divide by number of data - points. Kentucky temperatures: 57.5, 55.1, 52.2, 55.6, 55.0, 54.4, 54.5, 58.3, 57.3, 55.7. Sum = 57.5+55.1+52.2+55.6+55.0+54.4+54.5+58.3+57.3+55.7 = 555.6. Number of data - points = 10. Mean = $\frac{555.6}{10}=55.56$.

Step2: Calculate Kentucky median

Arrange Kentucky temperatures in ascending order: 52.2, 54.4, 54.5, 55.0, 55.1, 55.6, 55.7, 57.3, 57.5, 58.3. Since there are 10 (an even number) data - points, median is the average of the 5th and 6th ordered values. Median=$\frac{55.1 + 55.6}{2}=55.35$.

Step3: Compare with Illinois values

Illinois mean = 52.07, Illinois median = 51.85. Kentucky mean (55.56) > Illinois mean (52.07) and Kentucky median (55.35) > Illinois median (51.85).

Answer:

Kentucky mean = 55.56
Kentucky median = 55.35
Both measures of center for Kentucky are greater than those of Illinois.