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Chapter 3: Problem 40

Briefly explain the difference between a population parameter and a sample statistic. Give one example of each.

Short Answer

Expert verified
A population parameter is a characteristic that describes a feature of an entire population, such as the average height of all adults in a town, whereas a sample statistic describes a feature of a sample from that population, like the average height of students in a particular class, representing a sample from all students of the grade level in the school.

Step by step solution

01

Understanding Terms

Population parameter and sample statistic are two fundamental concepts in statistics. A population parameter refers to a characteristic that describes a particular feature of the entire population. It is a fixed value, but in most cases, it is not known because we cannot examine the entire population. On the other hand, a sample statistic is a characteristic that describes a particular feature of the sample drawn from the population. It is a variable quantity that changes from sample to sample.
02

Example of a Population Parameter

An example of a population parameter could be the average height of all adults in a town. The height of every single adult in the town would be measured, then those measurements would be averaged to give the population parameter.
03

Example of a Sample Statistic

An example of a sample statistic could be the average height of a class of students, which serves as a sample from the population of all students of the same grade level in a school. Here you wouldn't be able to measure the height of all the students of the grade level, instead, you measure the height of only the students in one class, and then calculate the average height. This average height is a sample statistic.

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Most popular questions from this chapter

The following data represent the numbers of tornadoes that touched down during 1950 to 1994 in the 12 states that had the most tornadoes during this period (Storm Prediction Center, 2009). The data for these states are given in the following order: CO, FL, IA, IL, KS, LA, MO, MS, NE, OK, SD, TX. \(\begin{array}{llllllllllll}1113 & 2009 & 1374 & 1137 & 2110 & 1086 & 1166 & 1039 & 1673 & 2300 & 1139 & 5490\end{array}\) a. Calculate the mean and median for these data. b. Identify the outlier in this data set. Drop the outlier and recalculate the mean and median. Which of these two summary measures changes by a larger amount when you drop the outlier? c. Which is the better summary measure for these data, the mean or the median? Explain.

The mean age of six persons is 46 years. The ages of five of these six persons are \(57,39,44,51\), and 37 years, respectively. Find the age of the sixth person.

The following data give the prices (in thousands of dollars) of 20 houses sold recently in a city. \(\begin{array}{llllllllll}184 & 297 & 365 & 309 & 245 & 387 & 369 & 438 & 195 & 390 \\ 323 & 578 & 410 & 679 & 307 & 271 & 457 & 795 & 259 & 590\end{array}\) Find the \(20 \%\) trimmed mean for this data set.

One disadvantage of the standard deviation as a measure of dispersion is that it is a measure of absolute variability and not of relative variability. Sometimes we may need to compare the variability of two different data sets that have different units of measurement. The coefficient of variation is one such measure. The coefficient of variation, denoted by CV, expresses standard deviation as a percentage of the mean and is computed as follows: For population data: \(\mathrm{CV}=\frac{\sigma}{\mu} \times 100 \%\) For sample data: \(\quad \mathrm{CV}=\frac{s}{\bar{x}} \times 100 \%\) The yearly salaries of all employees who work for a company have a mean of \(\$ 62,350\) and a standard deviation of \(\$ 6820\). The years of experience for the same employees have a mean of 15 years and a standard deviation of 2 years. Is the relative variation in the salaries larger or smaller than that in years of experience for these employees?

The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days. \(\begin{array}{llllllllll}45 & 52 & 48 & 41 & 56 & 46 & 44 & 42 & 48 & 53 \\\ 51 & 53 & 51 & 48 & 46 & 43 & 52 & 50 & 54 & 47 \\ 44 & 47 & 50 & 49 & 52 & & & & & \end{array}\) Prepare a box-and-whisker plot. Comment on the skewness of these data.
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