Concept explainers
Find (a) the mean, (b) the median, (c) the mode, and (d) the standard derivation of the following set of the raw material.
(a)
To find:
The mean of the following set of raw material.
Answer to Problem 1CR
Solution:
The mean of the given set of raw material is
Explanation of Solution
Given:
The given following set of raw material is,
Formula used:
The mean is the ratio of the sum of the data points to the number of the data points.
Consider the mean formula,
Here, the mean is
Calculation:
Consider the given set of raw materials,
Consider the total sum of the raw materials,
Consider the total number of data points,
Consider the mean formula,
Substitute
Thus, the mean of the given set of raw material is
Conclusion:
Thus, the mean of the given set of raw material is
(b)
To find:
The median of the following set of raw material.
Answer to Problem 1CR
Solution:
The median of the given data is
Explanation of Solution
Given:
The given following set of raw material is,
Formula used:
The median is the middle value of a distribution of numbers.
Consider the median position formula,
Here, the median number position is
Consider the median number formula,
Here, the median number is
Calculation:
Consider the given set of raw materials,
Consider the total number of data points,
Consider the mean formula,
Substitute
Thus, the median of the given set of raw material is
Consider the fifth raw material,
Consider the sixth raw material,
Consider the median number formula,
Substitute
Thus, the median of the given data is
Conclusion:
Thus, the median of the given data is
(c)
To find:
The mode of the following set of raw material.
Answer to Problem 1CR
Solution:
The mode of the given set of raw material is
Explanation of Solution
Given:
The given following set of raw material is,
Concept:
The mode is the data points with highest frequency. Because it represents the most common number, the mode can be viewed as an average.
Approach:
Consider the given set of raw materials,
The frequency of the number
The frequency of the number
The frequency of the number
The frequency of the number
The frequency of the number
The frequency of the number
Therefore, the mode is
Thus, the mode of the given set of raw material is
Conclusion:
Thus, the mode of the given set of raw material is
(d)
To find:
The standard derivation of the following set of raw material.
Answer to Problem 1CR
Solution:
The standard derivation of the given set of raw material is
Explanation of Solution
Given:
The given following set of raw material is,
Formula used:
The mean is the ratio of the sum of the data points to the number of the data points.
The variance of the sample is found by dividing the sum of squares of the deviations by
The square root of the variance is called standard variance.
Consider the mean formula,
Here, the mean is
Consider the variance formula,
Here, the variance is
Consider the standard formula,
Here, the standard deviation is
Calculation:
Consider the given set of raw materials,
Consider the total sum of the raw,
Consider the total number of data points,
Consider the mean formula,
Substitute
Thus, the mean of the given set of raw material is
Consider sum of squares of the deviations,
Consider the variance formula,
Substitute
Therefore, the variance is
Consider the standard formula,
Substitute
Thus, the standard deviation is
Conclusion:
Thus, the standard deviation is
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Chapter 4 Solutions
Mathematics: A Practical Odyssey
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill