Question

starting teachers’ salaries starting teacher salaries for upper secondary education in selected states are listed below.
starting salaries average salaries
alabama 31,368 alabama 40,347
alaska 38,657 alaska 53,553
arizona 30,404 arizona 44,672
arkansas 28,784 arkansas 42,768
california 35,760 california 59,825
colorado 35,086 colorado 44,439
connecticut 39,259 connecticut 59,304
delaware 35,854 delaware 54,264
florida 33,427 florida 43,302
georgia 34,442 georgia 48,300
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your answer
part: 0 / 3
part 1 of 3
find the range, variance, and standard deviation of starting salaries for 10 states. round your answers to at least one decimal place.
range = 10475
variance = 11,524,369.811
standard deviation = 3394.76

Explanation:

Step1: Calculate range (max-min)

Starting salaries: 28,784; 30,404; 31,368; 33,427; 34,442; 35,086; 35,760; 35,854; 38,657; 39,259
$\text{Range} = 39259 - 28784 = 10475$

Step2: Calculate mean of starting salaries

$\text{Mean} = \frac{28784+30404+31368+33427+34442+35086+35760+35854+38657+39259}{10}$
$\text{Mean} = \frac{343041}{10} = 34304.1$

Step3: Calculate squared deviations

For each salary $x_i$, compute $(x_i - \text{Mean})^2$:
$(28784-34304.1)^2 = (-5520.1)^2 = 30471504.01$
$(30404-34304.1)^2 = (-3900.1)^2 = 15210780.01$
$(31368-34304.1)^2 = (-2936.1)^2 = 8620683.21$
$(33427-34304.1)^2 = (-877.1)^2 = 769304.41$
$(34442-34304.1)^2 = (137.9)^2 = 19016.41$
$(35086-34304.1)^2 = (781.9)^2 = 611367.61$
$(35760-34304.1)^2 = (1455.9)^2 = 2119644.81$
$(35854-34304.1)^2 = (1549.9)^2 = 2392190.01$
$(38657-34304.1)^2 = (4352.9)^2 = 18947738.41$
$(39259-34304.1)^2 = (4954.9)^2 = 24549034.01$

Step4: Calculate population variance

Sum of squared deviations:
$30471504.01+15210780.01+8620683.21+769304.41+19016.41+611367.61+2119644.81+2392190.01+18947738.41+24549034.01 = 103701262.9$
$\text{Variance} = \frac{103701262.9}{10} = 10370126.3$

Step5: Calculate standard deviation

$\text{Standard Deviation} = \sqrt{10370126.3} \approx 3220.3$
(Note: If using sample variance, divide by 9: $\frac{103701262.9}{9} \approx 11522362.5$, standard deviation $\approx 3394.5$; but population variance is standard for full state dataset here.)

Answer:

Range = 10475
Variance = 10370126.3
Standard Deviation = 3220.3

*Note: If using sample statistics (dividing by n-1=9):
Variance = 11522362.5
Standard Deviation = 3394.5*