Three primary statistics are used to describe a variable's central tendency, defined as the average behavior of the variable. You can use these statistics, known as the mean, the median, and the mode, to draw meaningful conclusions about a variable's past behavior and to predict its future behavioc. An investor is considering a stock with the following returns over the past 12 years: Mean The mean, hiso known as the arithmetic mean, telis the observations and oivides by the number of observations, as shown in the following formula: korx=n22x The mean (or average) return for this stock over the past 12 years is For notational purposes, x, reprecents a same way. Median The medan indicates the observation in a data set. The med an tells us that half the data set lles above the median and the other hald lies below it. If you list all your observations in numenical ordet, the median would be the middle observation. for data sets with an odd number of observations, identiying the median is easy. However, for data sets with an even number of items, there is no "middle." In that case, you average the two middle: observations to find the median. Now, present the stock return data in ascending orderi 4%,5%,5%,6%,6%,6%,2%,8%,8%,9%,12%,14% This data set has 12 observations, so average observations 6 and to find the median, which is When the median and mean are sumiac, you cent conclude that the data is relatively symmetricat. Oepending on the distribution's thape, the dats may. be nocmally or uniformily distriboged. However, if the median is significantly less than of greater than the mean, that suggests that several extremely ignment 13: AOL Final HW be normally or uniformly distributed. However, if the median is significantly less than or greater than the mean, that suggests that several extremely high or low observations, called must be affecting the results, and that the distribution is skewed. Are there any outliers in this sample of data? Mode The mode indicates the observation. In the stock return data, the mode is because it occurs 3 times. The mode does not necessanly indicate the center of a data set, but if the data is roughly symmetrical, the mode will be close to the mean and medan. Check Your Understanding Your college football team has 15 linebackers listed on the roster. The weights of these 15 players, in pounds, are shown below: What is the weight of the average linebacker? What is the weight of the average linebacker? The is pounds. What weight is most common amongst the linebackers? The is pounds. What is the average welght of the linebackers? The is pounds