Question

52.1 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 behaviar An investor is considering a stock with the following returns over the past 12 years: Year Annual Return Year Annual Return 12 10 12 The mean, also known as the arithmetic mean, tells the The mean adds up all the observations and divides by the number of observations, as shown in the following formula value a variable is expected to take. The mean (or average) return for this stock over the past 12 years is For notational purposes, x-bar represents a However, they are calculated the same way. mean, while μ represents a The median indicates the lies above the median and the other half lies below it. observation in a data set. The median tells us that half the data set If you list all in an odd number of observations, identifying the median is easy. Howeve, 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. l your observations in numerical order, the median would be the middle observation, For data sets with Now, present the stock retum data in ascending order: 494, 5%, 5%, 6%,6%, 6%, 7%-89, 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 similar, you can conclude that the data is relatively symmetrical, Depending on the distribution's shape, the data may be normally ar 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? The modr indicates the because it occurs 3 times observation. In the stock return data, the mode is The mode does not necessarily indicate the center of a data set, but if the data is roughly symmetrical, the mode will be close to the mean and median. Check Your Understanding Your college football team has 15 linebackers listed on the roster. The weights of these 15 players are shown below: 238 219 233 208 236 227 220 208 227 225 241 248 227 215 What is the weight of the average linebacker? The What weight is most common amongst the linebackers? The What is the average weight of the linebackers? The

Answer 1

As per rules I am answering the first 4 subparts of the question

1: Average

(Mean represents the average value of a set of observations)

2: 7.5%

=(8%+12%+14%+8%+6%+6%+9%+5%+5%+4%+6%+7%)/ 12

=7.5%

3: Sample

X bar represents the mean of the sample and not the entire data.

4: Population

Mu represents the mean of the entire population.