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Chapter 3: Problem 10

Find the population mean or sample mean as indicated. Population: 1,19,25,15,12,16,28,13,6

Short Answer

Expert verified
The mean of the population is 15.

Step by step solution

01

Understand the Problem

The task is to find the mean of the given population. The mean is the average value of all numbers in the population.
02

Sum All the Numbers

Add all the numbers in the population together. Population: 1, 19, 25, 15, 12, 16, 28, 13, 6 Calculate the sum: \[ 1 + 19 + 25 + 15 + 12 + 16 + 28 + 13 + 6 = 135 \ \text{Sum} = 135 \]
03

Count the Numbers

Determine the number of values in the population. Here, there are 9 numbers.
04

Calculate the Mean

Divide the sum of all the numbers by the count of numbers. \[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{135}{9} = 15 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

mean
The mean is a central value of a set of numbers. To find the mean of any given population or sample, you primarily need two things: the sum of all values and the number of values in the dataset. When you divide the total sum by the number of values, you get the mean. For instance, in our exercise, the population data had values summed up to 135, and dividing by the 9 items gives us a mean of 15. This shows how the mean represents an average score or central tendency that balances all data points.
average
The terms 'mean' and 'average' are often used interchangeably in everyday language. Technically, the average can refer to different types of averages, such as mean, median, or mode. However, in most statistical contexts, when we discuss 鈥榓verage,鈥� we imply the arithmetic mean. This means adding all the values of a dataset and dividing by the number of values. Thus, the average in our exercise, calculated as 15, represents an evenly distributed central value.
sum of values
Summing values is the first crucial step in finding the mean. It involves adding all individual numbers in a dataset together. In our exercise, the population consists of values: 1, 19, 25, 15, 12, 16, 28, 13, and 6. Adding these values results in 135. This total is significant as it forms the numerator in the mean formula. Without a correct sum, it wouldn鈥檛 be possible to calculate an accurate mean.
population size
Population size denotes the total number of values in the dataset. This count is an essential factor in calculating the mean, as it serves as the divisor in the formula. For example, our dataset has 9 values, making the population size 9. This count tells us how many individual points we are averaging. Larger populations may give more accurate estimates of the mean, representing the central tendency more reliably.

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Most popular questions from this chapter

Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all 50 states in the United States plus Washington, D.C., in 2012 . $$ Q_{1}=252.4 \quad Q_{2}=333.8 \quad Q_{3}=454.5 $$ (a) Provide an interpretation of these results. (b) Determine and interpret the interquartile range. (c) The violent-crime rate in Washington, D.C., in 2012 was 1243.7. Would this be an outlier? (d) Do you believe that the distribution of violent-crime rates is skewed or symmetric? Why?

What does the five-number summary consist of?

The following data represent the pulse rates (beats per minute) of nine students enrolled in a section of Sullivan's Introductory Statistics course. Treat the nine students as a population. $$ \begin{array}{lc} \text { Student } & \text { Pulse } \\ \hline \text { Perpectual Bempah } & 76 \\ \hline \text { Megan Brooks } & 60 \\ \hline \text { Jeff Honeycutt } & 60 \\ \hline \text { Clarice Jefferson } & 81 \\ \hline \text { Crystal Kurtenbach } & 72 \\ \hline \text { Janette Lantka } & 80 \\ \hline \text { Kevin McCarthy } & 80 \\ \hline \text { Tammy Ohm } & 68 \\ \hline \text { Kathy Wojdyla } & 73 \\ \hline \end{array} $$ (a) Determine the population mean pulse. (b) Find three simple random samples of size 3 and determine the sample mean pulse of each sample. (c) Which samples result in a sample mean that overestimates the population mean? Which samples result in a sample mean that underestimates the population mean? Do any samples lead to a sample mean that equals the population mean?

True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has. provided that the variable of interest from the two populations has the same unit of measure.

Do store-brand chocolate chip cookies have fewer chips per cookie than Keebler's Chips Deluxe Chocolate Chip Cookies? To find out, a student randomly selected 21 cookies of each brand and counted the number of chips in the cookies. The results are shown next. $$ \begin{array}{lll|lll} &{\text { Keebler }} & && {\text { Store Brand }} \\ \hline 32 & 23 & 28 & 21 & 23 & 24 \\ \hline 28 & 28 & 29 & 24 & 25 & 27 \\ \hline 25 & 20 & 25 & 26 & 26 & 21 \\ \hline 22 & 21 & 24 & 18 & 16 & 24 \\ \hline 21 & 24 & 21 & 21 & 30 & 17 \\ \hline 26 & 28 & 24 & 23 & 28 & 31 \\ \hline 33 & 20 & 31 & 27 & 33 & 29 \\ \hline \end{array} $$ (a) Draw side-by-side boxplots for each brand of cookie. (b) Does there appear to be a difference in the number of chips per cookie? (c) Does one brand have a more consistent number of chips per cookie?
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