Explanation Definition: 1. While computing the mean of a frequency distribution, write all products x ⋅ f of the values and their frequencies in a new column of the table. Represent the sum of these products by ∑ ( x ⋅ f ) . Denote the sum of the frequencies by ∑ f . The mean is then ∑ ( x ⋅ f ) ∑ f . 2. If x is a data value in a set whose mean is x ¯ , then x − x ¯ is called x’s deviation from the mean. 3. We denote the standard deviation of a sample of n data values by s = ∑ ( x − x ¯ ) 2 n − 1 . 4. 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 mean of the given data set. To compute the mean, let us find all products x ⋅ f of the given values and their respective frequencies. For x = 2 and f = 1 , the product x ⋅ f = 2 ⋅ 1 = 2. For x = 3 and f = 1 , the product x ⋅ f = 3 ⋅ 1 = 3. For x = 4 and f = 0 , the product x ⋅ f = 4 ⋅ 0 = 0. For x = 5 and f = 2 , the product x ⋅ f = 5 ⋅ 2 = 10. For x = 6 and f = 3 , the product x ⋅ f = 6 ⋅ 3 = 18. For x = 7 and f = 4 , the product x ⋅ f = 7 ⋅ 4 = 28. For x = 8 and f = 4 , the product x ⋅ f = 8 ⋅ 4 = 32. For x = 9 and f = 3 , the product x ⋅ f = 9 ⋅ 3 = 27. For x = 10 and f = 2 , the product x ⋅ f = 10 ⋅ 2 = 20. The sum of these products is 2 + 3 + 0 + 10 + 18 + 28 + 32 + 27 + 20 = 140. Therefore, ∑ ( x ⋅ f ) = 140. The sum of the frequencies is 1 + 1 + 0 + 2 + 3 + 4 + 4 + 3 + 2 = 20. Therefore, ∑ f = 20. Therefore, the third column of the given table is as below. Number, x Frequency, f Product, x ⋅ f 2 1 2 3 1 3 4 0 0 5 2 10 6 3 18 7 4 28 8 4 32 9 3 27 10 2 20 ∑ f = 20 ∑ x ⋅ f = 140 The mean is then ∑ ( x ⋅ f ) ∑ f = 140 20 = 7

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Question

Chapter 14.3, Problem 11E

To determine

To find:

The mean and standard deviation and complete the table showing the number of fires per month in a city

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 10E

Chapter 14.3, Problem 12E

Students have asked these similar questions

Q/show that 2" +4 has a removable discontinuity at Z=2i Z(≥2-21)

Refer to page 100 for problems on graph theory and linear algebra. Instructions: • Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors. • Interpret the eigenvalues in the context of graph properties like connectivity or clustering. Discuss applications of spectral graph theory in network analysis. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]

Refer to page 110 for problems on optimization. Instructions: Given a loss function, analyze its critical points to identify minima and maxima. • Discuss the role of gradient descent in finding the optimal solution. . Compare convex and non-convex functions and their implications for optimization. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]

Chapter 14 Solutions

Mathematics All Around (6th Edition)

Knowledge Booster

The mean and standard deviation and complete the table showing the number of fires per month in a city

To find: The mean and standard deviation and complete the table showing the number of fires per month in a city

Want to see the full answer?

Chapter 14 Solutions

To find:

The mean and standard deviation and complete the table showing the number of fires per month in a city