a.
To identify: the sample and the population for each situation.
Then describe a statistic and a parameter.
a.
Answer to Problem 19PPS
The pennies chosen by Theo, Lydia and Peter each represents a sample and the total pennies in the jar, that is,
The mean year of the pennies in the sample is a statistic and the mean year of the pennies in the population is the parameter.
Explanation of Solution
Given information :
There are
The year of pennies in jar:
As per problem,
A sample is some portion of a larger group called population.
As per the given information, of the
The pennies chosen by Theo, Lydia and Peter each represents a sample and the total pennies in the jar, that is,
The mean year of the pennies in the sample is the statistic and the mean year of the pennies in the population is the parameter.
b.
To calculate: the mean year and mean absolute deviation of Theo’s pennies.
b.
Answer to Problem 19PPS
The mean year of Theo’s pennies is
The mean absolute deviation is
Explanation of Solution
Given:
There are
The years of Theo’s pennies are:
Formula used :
Step1: Find the mean,
Step2: Find the sum of the absolute values of the difference between each value in the set of data and the mean.
Step3: divide the sum by the number of values in the set of data.
Calculation:
As per the given problem,
The data set:
The number of values in the data set
Step1: To find the mean, add the values in the data and then divide by the number of values in the data set.
Step2: To find the sum of the absolute values, add the difference between each value and the mean.
The sum of absolute values
Step 3: Divide the sum by the number of values
c.
To calculate:the mean year and mean absolute deviation for Lydia’s pennies.
c.
Answer to Problem 19PPS
The mean year of Lydia’s pennies is
The mean absolute deviation is
Explanation of Solution
Given:
There are
The years of Lydia’s pennies are:
Calculation:
As per the given problem,
The data set:
The number of values in the data set
Step1: To find the mean, add the values in the data and then divide by the number of values in the data set.
Step2: To find the sum of the absolute values, add the difference between each value and the mean.
The sum of absolute values
Step 3: Divide the sum by the number of values
d.
To calculate: the mean year and mean absolute deviation for Peter’s pennies.
d.
Answer to Problem 19PPS
The mean year of Peter’s pennies is
The mean absolute deviation is
Explanation of Solution
Given:
There are
The years of Peter’s pennies are:
Calculation:
As per the given problem,
The data set:
The number of values in the data set
Step1: To find the mean, add the values in the data and then divide by the number of values in the data set.
Step2: To find the sum of the absolute values, add the difference between each value and the mean.
The sum of absolute values
Step 3: Divide the sum by the number of values
e.
To calculate: the mean year and mean absolute deviation for all the pennies in the jar.
To compare the samples with the full population.
e.
Answer to Problem 19PPS
The mean year of all the pennies is
The mean absolute deviation is
Peter’s sample is more similar to the full population than that of the others.
Explanation of Solution
Given:
There are
The year of pennies in jar:
Calculation:
As per the given problem,
The data set:
The number of values in the data set
Step1: To find the mean, add the values in the data and then divide by the number of values in the data set.
Step2: To find the sum of the absolute values, add the difference between each value and the mean.
The sum of absolute values
Step 3: Divide the sum by the number of values
As, Peter’s sample (calculate in part (d)) has the minimum difference from the population’s mean year (one year) and mean absolute deviation (
Chapter 12 Solutions
Algebra 1
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