Question

Each​ year, tornadoes that touch down are recorded. The following table gives the number of tornadoes that touched down during each month of one year. Determine the range and sample standard deviation.

4
3
51
123
197
95
67
93
64
64
102
107

Answer 1

SOLUTION:

From given data,

Each​ year, tornadoes that touch down are recorded. The following table gives the number of tornadoes that touched down during each month of one year.

	(-)	(-)2
4	(4-80.833) = -76.833	5903.309889
3	(3-80.833) = -77.833	6057.975889
51	(51-80.833) = -29.833	890.007889
123	(123-80.833) = 42.167	1778.055889
197	(197-80.833) = 116.167	13494.771889
95	(95-80.833) = 14.167	200.703889
67	(67-80.833) = -13.833	191.351889
93	(93-80.833) = 12.167	148.035889
64	(64-80.833) = -16.833	283.349889
64	(64-80.833) = -16.833	283.349889
102	(102-80.833) = 21.167	448.041889
107	(107-80.833) = 26.167	684.711889
= 970		(-)2 = 30363.666

= 4+3+51+123+197+95+67+93+64+64+102+107 =  970

Sample size = n = 12

= / n = 970/12 = 80.833

(-)²

= 5903.309889+6057.975889+890.007889+1778.055889+13494.771889+200.703889+191.351889+148.035889+283.349889+283.349889+448.041889+684.711889

= 30363.666

Determine the range and sample standard deviation.

The range

The range = Maximum value - Minimum value

Where,

Maximum value = 197

Minimum value = 3

The range = 197 - 3

The range = 194

sample standard deviation

sample standard deviation = S = sqrt((-)² / (n-1))

S = sqrt(30363.666 / (12-1))

S = sqrt(30363.666 /11)

S = 52.53887