# mean, median, mode

[1] Find the mean, median, and mode of the weights of bears given in Data Set 3 (this data set may be found in the back of your text).

[2] Find the standard deviation of the weights of bears given in Data Set 3. See attached

[3] Based on this data, at what weight would a bear be considered unusually heavy? How many of the bears are unusually heavy?

[4] What is the probability that a bear selected at random would be unusually heavy? What is the probability that a bear selected at random would not be unusually heavy?

[5] What is the probability that a bear selected at random has a weight less than 200 pounds or greater than 60 pounds?

[6] Organize the weights of bears into a frequency table with seven weight classes.

[7] From your frequency table create a frequency histogram and a relative frequency histogram. (You will need information from your relative frequency histogram to help answer problem 8 below.)

[8] What is the probability that a bear's weight would fall into the third weight class? What is the probability that four bears, picked at random, will have weights that fall into the third weight class?

[9] Seven bears are to be randomly selected for "Special Bear Testing." How many different groups of bears are possible?

[10] What is the probability that the first seven bears will be selected for special testing?

What is the probability that the last seven bears will be selected for special testing?

All of the analysis above depends on a getting a good sample. What sampling issues would you need to address to make sure your results are reliable?

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#### Solution Preview

Please see the attached files.

[1] Find the mean, median, and mode of the weights of bears given in Data Set 3 (this data set may be found in the back of your text).

We can use EXCEL command (or any other statistical software you like) to calculate these values:

Please refer to the EXCEL for calculation.

Mean is an estimator available for estimating the average value. Mean = 182.89

The median is the value halfway through the ordered data set, below and above which there lies an equal number of data values. Median = 150

The mode is the most frequently occurring value in a set of discrete data. There can be more than one mode if two or more values are equally common. Mode = 166

[2] Find the standard deviation of the weights of bears given in Data Set 3. See attached

Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated by taking the square root of the variance and is symbolised by s.d

That is: SD = 121.80

[3] Based on this data, at what weight would a bear be considered unusually heavy? How many of the bears are unusually heavy?

A measurement in a statistical study is said to be statistically unusual, if it is unlikely to have occurred by chance. We say that a bear is statistically unusually heavy at the .05 level if the ...

#### Solution Summary

The mean, median, and mode of the weights of bears given in Data Set 3 (this data set may be found in the back of your text) is found. The standard deviation of the weights of bears given in Data Set 3 is determined.