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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola
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Solved: Finding Standard Deviation from a Frequency

Chapter 3, Problem 38BSC

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QUESTION:

Finding Standard Deviation from a Frequency Distribution. In Exercises 37–40, find the standard deviation of sample data summarized in a frequency distribution table by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3­4 with the original list of data values: (Exercise 37) 11.1 years; (Exercise 38) 9.0 years; (Exercise 39) 13.4; (Exercise 40) 9.7 years. 

     \(s=n[\Sigma(f \cdot x 2)]-[\Sigma(f \cdot x)] 2 n(n-1)\) Standard deviation for frequency distribution

Equation Transcription:

Text Transcription:

s=n[\Sigma(f \cdot x 2)]-[\Sigma(f \cdot x)] 2 n(n-1)

Questions & Answers

QUESTION:

Finding Standard Deviation from a Frequency Distribution. In Exercises 37–40, find the standard deviation of sample data summarized in a frequency distribution table by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3­4 with the original list of data values: (Exercise 37) 11.1 years; (Exercise 38) 9.0 years; (Exercise 39) 13.4; (Exercise 40) 9.7 years. 

     \(s=n[\Sigma(f \cdot x 2)]-[\Sigma(f \cdot x)] 2 n(n-1)\) Standard deviation for frequency distribution

Equation Transcription:

Text Transcription:

s=n[\Sigma(f \cdot x 2)]-[\Sigma(f \cdot x)] 2 n(n-1)

ANSWER:

Problem 38BSC

Answer:

Step1 of 3:

We have standard deviation for frequency distribution

s =

Where,

 x  represents the class midpoint,

 f   represents the class frequency, and

 n  represents the total number of sample values.

Age of Best Actor When Oscar
 Was

Frequency

20–29

1

30–39

26

40–49

35

50–59

13

60–69

6

70–79

1

Step2 of 3:

We need to find the standard deviation of sample data summarized in a frequency distribution table by using the formula below,also, compare the computed standard deviations to these standard deviations obtained by using Formula 3-4 with the original list of data values. 11.1 years.

Step3 of 3:

Consider,

Age of Best Actor When Oscar
 Was

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