Three primary statistics are used to describe a varlable's central tendency, defined as the average behavior of the varlable, 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 behavior. An investor is considering a stock with the following returns over the past 12 years: The mean, also known as the arithmetic mean, tells the value a variable is expected to take. The mean adds up all the observations and divides by the number of observations, as shown in the following formula: orx=n2,1 The mean (or average) retuen for this stock over the past 12 years is For notational purposes, x represents a same nay. mean, while represents a mean. However, they are calculated the Median The median indirates the ether half lies below it. otservation in a data set. The median teils in that hay the data set les above the median and the If you int all your observatoons in numericel ocder, the median would be the middle observation. For dats sets with an odd number of obseryation, identifing the median is easy. Monever, for data sets with an even number of items, there is no "midde. "In that raie. you arierage the tave midife cbservations to find the medien. Now, Brewent the stock return data in ascending order, 4%,5%,5%,6%,6%,6%,7%,8%,6%,9%,12%,1446 This data set has 12, observations, so average observations 6 and to find the median, which is When the median and mean are similar, you can conclude that the data is relathely symmetrical. Depending on the distribution's shape, the data may 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 outlers in this sample of data? Mode The mode indicates the observation. In the stock return data, the mode is because it occurs 3 tmes. The mode does not pecessarily indicate the cemer of a data set, but if the data is roughly sym. arical, the mede wilt be cose to the mean and mediaf. Check. Your Understanding Your college football team has 15 tinebackers fisted on the roster, The weights of these 15 players, in pounds, are shown belon: 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? The pounds. What weight is most common amongst the linebackers? The is pounds. What is the average weight of the linebackers? The pounds