Therefore, the average price of items sold was about $15.19. Dividing that sum by the number of measurements yields the sample mean for grouped data.įor example, consider the information shown in Table 3. Σ fx denotes the sum of all the products in all class intervals. Where x is the midpoint of the interval, f is the frequency for the interval, fx is the product of the midpoint times the frequency, and n is the number of values.įor example, if 8 is the midpoint of a class interval and there are ten measurements in the interval, fx = 10(8) = 80, the sum of the ten measurements in the interval. The formula for a sample mean for grouped data is Although you do not have precise individual measures, you still can compute measures for grouped data, data presented in a frequency table. This type of information is similar to that presented in a frequency table. For example, you may know that, in a certain working population, 32 percent earn between $25,000 and $29,999 40 percent earn between $30,000 and $34,999 27 percent earn between $35,000 and $39,999 and the remaining 1 percent earn between $80,000 and $85,000. Occasionally, you may have data that consist not of actual values but rather of grouped measures. The sum (or total) of measures is typically denoted with a Σ. The mean of a population is typically denoted as μ (pronounced mew). The mean of a sample is typically denoted as (read as x bar). In the set of weekly earnings in Table 1, the mode would be $350 because it appears twice and the other values appear only once. In this instance, the median appears to be a better indicator of central tendency because the CEO's salary is an extreme outlier, causing the mean to lie far from the other three salaries.Īnother indicator of central tendency is the mode, or the value that occurs most often in a set of numbers. The median is the average of the middle two salaries, or $40,000. The mean of these four salaries is $275,000. Given the four annual salaries of a corporation shown in Table 2, determine the mean and the median. The median may sometimes be a better indicator of central tendency than the mean, especially when there are outliers, or extreme values. For example, if we had four values-4, 10, 12, and 26-the median would be the average of the two middle values, 10 and 12 in this case, 11 is the median. If there is an even number of items in a set, the median is the average of the two middle values. The middle value is $150 therefore, $150 is the median. When you order the daily earnings shown in Table 1, you get $50, $100, $150, $350, and $350. Totaling all the measures and dividing by the number of measures, you get $1,000 ÷ 5 = $200.Īnother measure of central tendency is the median, which is defined as the middle value when the numbers are arranged in increasing or decreasing order. The arithmetic mean is the sum of the measures in the set divided by the number of measures in the set. One way is to use the average, or mean, of the data set. You could express your daily earnings from Table 1 in a number of ways. Three such middle numbers are the mean, the median, and the mode.įor example, suppose your earnings for the past week were the values shown in Table 1. Measures of central tendency are numbers that tend to cluster around the “middle” of a set of values. Quiz: Test for Comparing Two Proportions.Quiz: Test for a Single Population Proportion.Test for a Single Population Proportion.Quiz: Two-Sample t-test for Comparing Two Means.Two Sample t test for Comparing Two Means.Quiz: Two-Sample z-test for Comparing Two Means.Quiz: Introduction to Univariate Inferential Tests.Two-Sample z-test for Comparing Two Means.Quiz: Point Estimates and Confidence Intervals.

Point Estimates and Confidence Intervals.Quiz: Normal Approximation to the Binomial.

Quiz: Populations, Samples, Parameters, and Statistics.

Populations, Samples, Parameters, and Statistics.

Quiz: Introduction to Numerical Measures.

Define point measure in statistics