This lesson will show how the value of the standard deviation or σ gives the spread of a normal distribution. Recall that in the lessons about measures of dispersion and standard deviation, we saw that the bigger the standard deviation, the bigger the spread. Well, this may help us understand the spread of a normal […]
You can use the central limit theorem when sampling from a population that is not normally distributed. Most of the time the population from which the samples are selected is not going to be normally distributed. However, as the sample size increases, the sampling distribution of x̄ will approach a normal distribution. Central limit theorem […]
Before explaining what an unbiased estimator is, let us explain what an estimator is. An estimator is a value or range of values used to estimate or approximate a population parameter. For example, we call the sample mean, x̄ , an estimator of the population mean or μ. It turns out that the sample mean […]
What can we conclude when sampling from a normally distributed population?In other words, what can we conclude about samples drawn from a normally distributed population with mean equal to μ and standard deviation equal to σ ? The followings hold true: a. The mean of x̄ or μx̄ is equal to the mean of the […]
The standard deviation of the sampling distribution of x̄ is is where σ is the standard deviation of the population and n is the sample size. Notice that unlike the mean of the sampling distribution of x̄ which is equal to the mean of the population, the standard deviation, σx̄, of x̄ is not equal […]
Review the lesson about Midrange of a data set carefully before taking this quiz. When answering questions, keep in mind that there may be more than 1 correct answer.
Review the lesson about mode of a data set carefully before taking this quiz. When answering questions, keep in mind that there may be more than 1 correct answer.
Review the lesson about median of a set of data carefully before taking this quiz. When answering questions, keep in mind that there may be more than 1 correct answer.
Review the lesson about mean from a frequency table carefully before taking this quiz. When answering questions, keep in mind that there may be more than 1 correct answer.
Review the lesson about Arithmetic mean carefully before taking this quiz. When answering questions, keep in mind that there may be more than 1 correct answer.
Review the lesson about Types of variables carefully before taking this quiz. When answering questions, keep in mind that there may be more than 1 correct answer.
Review the lesson about Variable, element, data set, and observation carefully before taking this quiz.
Review the lesson about Common sampling methods carefully before taking this quiz.
Review the lesson about representative sample carefully before taking this quiz.
Review the lesson about what is a survey carefully before taking this quiz.
Review the lesson about population versus sample carefully before taking this quiz.
Review the lesson about types of statistics carefully before taking this quiz.
Review the lesson about what is statistics carefully before taking this quiz
Here we show some examples of binomial experiments. But before we do so, what is a binomial experiment? When an experiment satisfies the following four conditions, the experiment is called a binomial experiment. Now, we will show a couple of good examples of binomial experiments to illustrate the concept. Example #1 Consider the experiment of […]
Find here some normal distribution word problems or some applications of the normal distribution. Example #1 Suppose the current annual salary of all teachers in the United States have a normal distribution with a mean of 51000 dollars and a standard deviation of 6000 dollars. Find the probability that the annual salary of a randomly […]
Finding the z-scores for a specified area is the reverse procedure of finding the area under the normal curve. You will again need the standard normal distribution table Example #1 Find a point z such that the area under the standard normal curve between 0 and z is 0.3749 and the value of z is […]
Standardizing a normal distribution is to convert a normal distribution to the standard normal distribution. In real-world applications, a continuous random variable may have a normal distribution with a value of the mean that is different from 0 and a value of the standard deviation that is different from 1. In this case, we need […]
Learn how to calculate the area under the standard normal curve. This is an important skill, so study the following examples carefully. You will need the standard normal distribution table to solve problems. So go ahead and print the table and come back here. Example #1 Find the area under the curve between z = […]
Here is the standard normal distribution table. The entries give the areas under the standard normal curve from 0 to z. z .00 .01 .02 .03 .04 .05 […]
The standard normal distribution (SND) is a special case of the normal distribution. When a normally distributed variable has a mean of 0 and a standard deviation of 1, we call this distribution standard normal distribution. The random variable is denoted by z. In other words, notice that we use z instead of x […]
The normal probability distribution, also called normal curve, is a special type of bell-shaped curve like the one you see here. A continuous random variable is normally distributed either exactly or approximately. For example, scores on examination and heights of people are normally distributed. Characteristics of a normal distribution a. The total area under the […]
The continuous probability distribution is a table that shows the frequency and relative frequency of a continuous random variable. Recall that a continuous random variable can take any value over an interval or intervals. For example, suppose students have 60 minutes to finish a test. The time it takes students to finish the test can […]
The mean of the sampling distribution of x̄ (also called mean of x̄) is the mean of all possible sample means. In the lesson about sampling distribution, we ended up with the following sampling distribution of x̄ x̄ P(x̄) 83.33 0.10 85 0.20 85.66 0.20 86.66 0.10 87.33 0.20 89 0.20 ∑P(x̄) = 1 What if […]
This lesson will show the difference between sampling and nonsampling errors. Using a sample in order to get information about a population is often better than conducting a census for many reasons. Sampling is less costly and it can be done more quickly than a census which requires data for the entire population. However, as […]
As stated in the previous lesson, the population mean is always constant. However, different samples of the same size drawn from the population will yield different values for the sample mean or x̄ . Consequently, the sample mean, x̄ , is a random variable and just like any other random variables, the sample mean x̄ has […]
The population distribution is the probability distribution using all elements of a population. Suppose there are 5 students in a math class and their scores on the final exam are 80 85 85 90 92 The 5 scores above are the scores for the population since we are using all 5 scores. Let x be […]
The Poisson probability distribution is named after the French mathematician Simeon D. Poisson. Suppose there is a power outage in an apartment complex 3 times a year. You may want to find the probability that there will be exactly 2 power outage next year. This is an example of a Poisson probability distribution problem. Each […]
Here is a list of the types of averages used in statistics also called or measures of central tendency. We start with the common type. The most common types of averages are the mean, median, and mode. Mean The mean is found by adding all the numbers in a list and then divide by how […]
Summation notation is used to denote the sum of values. Suppose you have a sample consisting of the ages of 5 students in a middle school. Suppose the ages of these five students are 12, 14, 15, 10, and 9 The variable age of a student can be denoted by x You could write the […]
The mode of a data set is the value that occurs most frequently. In other words, you are looking for the value with the highest frequency. The following data set gives the number of hours kids spend on homework every night. 2 3 4 1 […]
The median of a set of data is the middle value after the data set has been ranked either in increasing or decreasing order. The symbol used for the median is . We pronounce as “x-tilde.” Since the median is the middle value, it divides a ranked data set into two equal parts. There are two […]
A stem-and-leaf display can also be used to organize only quantitative data. What do we mean though by stem and leaf? We can divide the number 56 into a stem and a leaf. 5 is the stem and 6 is the leaf. How do we divide though the number 9 though into a stem and […]
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