Q 3.73. Determine the age and sample sta... [FREE SOLUTION]

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Chapter 3: Q 3.73. (page 114)

Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation.
Tornado Touchdowns. Each year, tornadoes that touch down are recorded by the Storm Prediction Center and published in Monthly Tornado Statistics. The following table gives the number of tornadoes that touched down in the United States during each month of one year.
$3, 2, 47, 118, 204, 97, 68, 86, 62, 57, 98, 99$

Short Answer

Expert verified

Range of the data $= 202$

Standard deviation of the data $= 53.8 t o r n a d o e s$

Step by step solution

Step 1. Given information.

We have given data: $3, 2, 47, 118, 204, 97, 68, 86, 62, 57, 98, 99$ .

Step 2. To find range of the data.

$R a n g e = M a x . v a l u e - M i n . v a l u e = 204 - 2 = 202$

Step 3. To find mean of the data.

$M e a n = \frac{S u m o f t h e o b s e r v a t i o n}{N u m b e r o f o b s e r v a t i o n} = \frac{3 + 2 + 47 + 118 + 204 + 97 + 68 + 86 + 62 + 57 + 98 + 99}{12} = \frac{941}{12} = 78.41$

Step 4. To find standard deviation of the data.

$x$	$(x - x)$	${(x - x)}^{2}$
$3 2 47 118 204 97 68 86 62 57 98 99$	$- 75.4 - 76.4 - 31.4 39.6 125.6 18.6 - 10.4 7.6 - 16.4 - 21.4 19.6 20.6$	$5685.16 5836.96 985.96 1568.16 15775.36 345.96 108.16 57.76 268.96 457.96 384.16 424.36$