Question

The data set shown here

Class Frequency

[70,74.9] 3 |||

[75,79.9] 8 ||||||||

[80,84.9] 7 |||||||

[85,89.9] 9 |||||||||

[90,94.9] 14 ||||||||||||||

[95,99.9] 16 ||||||||||||||||

[100,104.9] 13 |||||||||||||

[105,109.9] 15 |||||||||||||||

[110,114.9] 21 |||||||||||||||||||||

[115,119.9] 7 |||||||

[120,124.9] 6 ||||||

[125,129.9] 2 ||

[130,134.9] 3 |||

[135,139.9] 0

[140,144.9] 0

[145,149.9] 0

[150,154.9] 1 |

has the five number summary {70.7, 92, 102.6, 112, 153.9}

Using this information, approximate the standard deviation for the data set using the count-by-thirds empirical rule.

Standard Deviation ≈

Note: The actual standard deviation for this data is 14.7705. How would you rate your approximation, ¿good or bad?

Answer 1

standard deviation can be apprpoximated by IQR

IQR=Q3-Q1

= 112-92

= 20

and standard deviation = IQR/1.35

= 20/1.35

= 14.81

and actual standard deviation = 14.77

which is close.

therefore approximation is good.