Bring fact-checked results to the top of your browser search. Estimation of a population mean The most fundamental point and interval estimation process involves the estimation of a population mean.
Year 8 Statistics and population mean Maths - Second Edition Mean, Median and Mode We use statistics such as the meanmedian and mode to obtain information about a population from our sample set of observed values.
Mean The mean or average of a set of data values is the sum of all of the data values divided by the number of data values. Example 1 The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: So, the mean mark is Symbolically, we can set out the solution as follows: Median The median of a set of data values is the middle value of the data set when it has been arranged in ascending order.
That is, from the smallest value to the highest value. Example 2 The marks of nine students in a geography test that had a maximum possible mark of 50 are given below: Arrange the data values in order from the lowest value to the highest value: If the number of values in the data set is even, then the median is the average of the two middle values.
Example 3 Find the median of the following data set: So, the median is the average of the two middle values. There are 8 values in the data set. The fourth and fifth scores, 16 and 17, are in the middle.
That is, there is no one middle value. Half of the values in the data set lie below the median and half lie above the median. The median is the most commonly quoted figure used to measure property prices. The use of the median avoids the problem of the mean property price which is affected by a few expensive properties that are not representative of the general property market.
Mode The mode of a set of data values is the value s that occurs most often.
The mode has applications in printing. For example, it is important to print more of the most popular books; because printing different books in equal numbers would cause a shortage of some books and an oversupply of others.
Likewise, the mode has applications in manufacturing. For example, it is important to manufacture more of the most popular shoes; because manufacturing different shoes in equal numbers would cause a shortage of some shoes and an oversupply of others.
Example 4 Find the mode of the following data set: The mode is 48 since it occurs most often.
It is possible for a set of data values to have more than one mode. If there are two data values that occur most frequently, we say that the set of data values is bimodal. If there is no data value or data values that occur most frequently, we say that the set of data values has no mode.
Analysing Data The meanmedian and mode of a data set are collectively known as measures of central tendency as these three measures focus on where the data is centred or clustered. To analyse data using the mean, median and mode, we need to use the most appropriate measure of central tendency.
The following points should be remembered:noun Statistics. a quantity or statistical measure that, for a given population, is fixed and that is used as the value of a variable in some general distribution or frequency function to make it descriptive of that population: The mean and variance of a population are population parameters.
Inferring a population mean from a sample mean Join Curt Frye for an in-depth discussion in this video, Inferring a population mean from a sample mean, part of Excel Business Statistics. For the sake of illustration, assume that you're using a 1-sample t-test to determine whether the population mean is greater than a hypothesized value, such as 5, based on a sample of 20 observations, as shown in the above t-test output.
Estimation of a population mean. The most fundamental point and interval estimation process involves the estimation of a population mean. Suppose it is of interest to estimate the population mean, μ, for a quantitative variable. For both population and sample variance, I calculate the mean, then the deviations from the mean, and then I square all the deviations.
I sum all the squared deviations up. So far it was the same for both population and sample variance.
The sampling distribution of the mean refers to the pattern of sample means that will occur as samples are drawn from the population at large Example I want to.