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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

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?

Explain how to determine the shape of a distribution using the box plot and quartiles.

For each of the following situations, determine which measure of central tendency is most appropriate and justify your reasoning. (a) Average price of a home sold in Pittsburgh, Pennsylvania, in 2011 (b) Most popular major for students enrolled in a statistics course (c) Average test score when the scores are distributed symmetrically (d) Average test score when the scores are skewed right (e) Average income of a player in the National Football League (f) Most requested song at a radio station (g) Typical number on the jersey of a player in the National Hockey League.

The data below represent the age of the mother at the time of her first birth for a random sample of 30 mothers. $$ \begin{array}{llllll} \hline 21 & 35 & 33 & 25 & 22 & 26 \\ \hline 21 & 24 & 16 & 32 & 25 & 20 \\ \hline 30 & 20 & 20 & 29 & 21 & 19 \\ \hline 18 & 24 & 33 & 22 & 23 & 25 \\ \hline 17 & 23 & 25 & 29 & 25 & 19 \\ \hline \end{array} $$ (a) Construct a box plot of the data. (b) Use the box plot and quartiles to describe the shape of the distribution.

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?
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