Question

Use the​ F-scale measurements of tornadoes listed in the accompanying table. The range of the data is 4.0. Use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the actual standard deviation of the​ data, 1.0.

3
2
3
2
1
1
0
1
2
3
1
1
1
2
2
2
2
0
1
2
1
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
1
2
3
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
2
4
0
1
0
0
0
0
2
2
0
1
1

1
2
1
0
0
2
0
2
0
2
2
2
0
0
4
0
Compare the result to the actual standard deviation.
The estimated standard deviation is________(within 0.5 of, over 0.5 less than, over 0.5 greater than) the actual standard deviation.​ Thus, the estimated standard deviation_________(is, is not) substantially different from the actual standard deviation.

Answer 1

Within 0.5 of ;

is not ;

Explanation:

Given the data:

The actual standard deviation, = 1

;

The range rule of thumb to estimate the value if standard deviation is ;

Estimated standard deviation = Range / 4

The range = (maximum - minimum) values

The estimated standard deviation = 4 / 4 = 1

Hence, the estimated standard deviation is with 0.5 of the actual standard deviation, Thus, the estimated standard deviation is not substantially different from the actual standard deviation.