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Chapter 3: Problem 7

Find the population mean or sample mean as indicated. Sample: 20,13,4,8,10

Short Answer

Expert verified
The sample mean is 11.

Step by step solution

01

Understand the Problem

We are given a sample set of data and need to find the sample mean. The given sample is: 20, 13, 4, 8, 10.
02

Sum the Data Points

Add up all the data points in the sample. \[ 20 + 13 + 4 + 8 + 10 = 55 \]
03

Count the Number of Data Points

Count how many data points are in the sample. There are 5 data points.
04

Calculate the Sample Mean

Divide the sum of the data points by the number of data points. \[ \text{Sample Mean} = \frac{\text{Sum of Data Points}}{\text{Number of Data Points}} = \frac{55}{5} = 11 \]

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Key Concepts

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

Sample Mean
The sample mean is a measure of the average value of a set of data points. It is calculated by summing all the data points in the sample and then dividing that sum by the number of data points. This is a fundamental concept in statistics and is especially useful in making inferences about a population based on a sample. For instance, if we have a sample data set: 20, 13, 4, 8, and 10, we can find the sample mean to understand the central tendency of this data. Calculating the sample mean helps to summarize the data with a single value that represents the 'central' or 'average' value of the dataset.
Data Points
Data points are individual values in a dataset. When we talk about calculating the sample mean, we're dealing with each value in the sample. In our example, the data points are 20, 13, 4, 8, and 10. It's important to understand that each data point contributes equally to the sum, regardless of its magnitude. When counting data points, it helps to ensure that we don't miss any values, as the number of data points (N) is crucial for calculating the sample mean accurately. In our case, there are 5 data points.
Sum of Data Points
Summing the data points means adding all the individual values in a dataset together. This is a simple yet essential step in calculating the sample mean. For example, given the data points 20, 13, 4, 8, and 10, you add them together: 20 + 13 + 4 + 8 + 10 = 55 Once you have the total sum of the data points, you can proceed to determine the mean by dividing this sum by the number of data points. The sum of the data points gives a crucial piece of information about the dataset and acts as the intermediary step in most basic statistical calculations, including variance and standard deviation.

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Most popular questions from this chapter

The average 20 - to 29 -year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20 - to 29 -year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75 -inch man or a 70 -inch woman?

The following data represent the diagnosis of a random sample of 20 patients admitted to a hospital. Determine the mode diagnosis. $$ \begin{array}{lll} \hline \text { Cancer } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \begin{array}{l} \text { Congestive heart } \\ \text { failure } \end{array} \\ \hline \text { Gunshot wound } & \text { Fall } & \text { Gunshot wound } \\ \hline \text { Gunshot wound } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \text { Assault } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \text { Fall } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} \\ \hline \text { Source: Tamela Ohm, student at Joliet Junior College } \end{array} $$

What makes the range less desirable than the standard deviation as a measure of dispersion?

A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The strength of concrete is measured by pouring the mix into casting cylinders after it is allowed to set up for 28 days. The following data represent the strength of nine randomly selected casts. Compute the range and sample standard deviation for the strength of the concrete (in psi). $$ 3960,4090,3200,3100,2940,3830,4090,4040,3780 $$

The following data represent the weight (in grams) of a random sample of 25 Tylenol tablets. $$ \begin{array}{lllll} \hline 0.608 & 0.601 & 0.606 & 0.602 & 0.611 \\ \hline 0.608 & 0.610 & 0.610 & 0.607 & 0.600 \\ \hline 0.608 & 0.608 & 0.605 & 0.609 & 0.605 \\ \hline 0.610 & 0.607 & 0.611 & 0.608 & 0.610 \\ \hline 0.612 & 0.598 & 0.600 & 0.605 & 0.603 \\ \hline \end{array} $$ (a) Construct a box plot. (b) Use the box plot and quartiles to describe the shape of the distribution.
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