Explanation Definition: 1. The range of a data set is the difference between the largest and smallest data values in the set. 2. If a data set contains n data values, the mean x ¯ of the data set is x ¯ = ∑ x n . 3. If x is a data value in a set whose mean is x ¯ , then x − x ¯ is called x’s deviation from the mean. 4. We denote the standard deviation of a sample of n data values by s = ∑ ( x − x ¯ ) 2 n − 1 . 5. We calculate the standard deviation, s, of a sample that is given as a frequency distribution as s = ∑ ( x − x ¯ ) 2 ⋅ f n − 1 . Here f is the frequency of data value x , and n = ∑ f is the number of data values in the distribution. Calculation: First find the range of the given data set. The largest data value is 6 and the smallest data value is 4. Since range is the difference between the largest and the smallest data value, the range of given data is 6 − 4 = 2. Next find the mean of the given data set. Begin by finding the sum of the given data. Sum of 4, 6, 4, 6, 4, 6, 4, and 6 is 40. There are 8 values in the given data. Therefore, the mean is x ¯ = 40 8 = 5. Now find the standard deviation. Observe that there are some repeated values in the given data. Therefore, we will use a frequency table to compute the standard deviation. The frequency of 4 is 4. That is, 4 comes four times in the data set. Similarly, the frequency of 6 is 4. Now find the product x ⋅ f for each data value. Notice that 4 ⋅ 4 = 16 , and 6 ⋅ 4 = 24. The deviation is the difference between each product value and the mean. Therefore, the deviation of 4 from the mean 5 is 4 − 5 = − 1

6th Edition

ISBN: 9780134506470

Author: 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 14.3, Problem 10E

To determine

To find:

The range, mean, and standard deviation for the following data set:

4, 6, 4, 6, 4, 6, 4, 6

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 9E

Chapter 14.3, Problem 11E

Students have asked these similar questions

For all integers a and b if a is congruent to 0(mod n) and b is congruent to 0(mod n) then a+b is congruent 0(mod n) DRAW A KNOW-SHOW TABLE:

Phase 1C: Question Writing and Approval Based on either your own discussion post or ideas sparked from what others mentioned, select two questions you’d like to answer by analyzing data from Census at School. You will need to select one question from the qualitative category, and one question from the quantitative category. Remember the intent of these questions is to make comparisons and analyze data to eventually make inferences about and possibly draw conclusions about the larger population. You should make notes as you gather your data on what things might be missing, what factors might be contributing to this data, and what questions you still have. Qualitative Only Options How are males and females similar or different in their favorite subjects in school? Quantitative Options Do the number of texts sent differ between freshmen and seniors in high school?

0 2nπ 1 {| sin x|-|sin x]}dx 2

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 range, mean, and standard deviation for the following data set: 4, 6, 4, 6, 4, 6, 4, 6

Solution Summary: The author explains that the range of a data set is the difference between the largest and smallest data values.

Concept explainers

Videos

To find: The range, mean, and standard deviation for the following data set: 4, 6, 4, 6, 4, 6, 4, 6

Want to see the full answer?

Chapter 14 Solutions

To find:

The range, mean, and standard deviation for the following data set:

4, 6, 4, 6, 4, 6, 4, 6