Explanation Definition: Standard deviation: Suppose x is a data value in a set whose mean is x ¯ , then x − x ¯ is called x ’s deviation from mean. The formula for standard deviation of a sample n data values is s = ∑ ( x − x ¯ ) 2 n − 1 . Mean: Suppose the data set contains n data values, the mean x ¯ of the data is computing by the formula x ¯ = ∑ x n . Calculation: Standard deviation is a reliable measure of dispersion. It is a number and used to tell about the measurements for a group of data. That is the spread out from the average value or mean or expected value by using the definition mentioned above. The low standard deviation denotes that most of the numbers are close to the average. The high standard deviation denotes that the numbers are more spread out. Example: The given distribution is 8 , 6 , 7 , 6 , 4 , 5 . Compute the mean for the distribution 8 , 6 , 7 , 6 , 4 , 5 . Here, n = 8 . Compute the mean of the distribution by using the mean formula mentioned above. x ¯ = 8 + 6 + 7 + 6 + 4 + 5 8 = 36 6 = 6 Therefore, the mean of the distribution is x ¯ = 6 . Compute the squares of the deviations of the data values from the mean as shown in below table

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Chapter 14.CR, Problem 11CR

To determine

To explain:

The standard deviation tells about a distribution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.CR, Problem 10CR

Chapter 14.CR, Problem 12CR

Students have asked these similar questions

18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0<|z|< 1, f(E) f(E) 2πif(z) = --- d.

Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.

18.4. Let f be analytic within and on a positively oriented closed contoury, and the point zo is not on y. Show that L f(z) (-20)2 dz = '(2) dz. 2-20

Chapter 14 Solutions

Mathematics All Around (6th Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The standard deviation tells about a distribution.

Solution Summary: The author explains that standard deviation is a reliable measure of dispersion.

Concept explainers

Videos

To explain: The standard deviation tells about a distribution.

Want to see the full answer?

Chapter 14 Solutions

To explain:

The standard deviation tells about a distribution.