The first step with analyzing data is to make sure the all data values were sbumitted correctly and seem to be reasonable$/$proper measurements$$this is called cleaning the data. In initial analysis of the student data, there were several mismeasurments or incorrectly given measurements; much of this was cleaned already. More formally one would also look for possible outliers using a process $($like the $1\mathrm{.}5$IQR rule$)$ and decide whether or not to include these data in further analysis. In general, a valid and well established argument should always be given for removal of any data from a data set; removal of any collected data should NOT be done arbitrarily or to skew the data to some desired viewpoint. Analyze the data given in the ATTACHED worksheet $($see this worksheet below as "Original Data Set for Analysis"$).$ Using the $1\mathrm{.}5$IQR rule discussed in the first unit $($text Section $4\mathrm{.}3),$ find the one outlier within the Footlength variable. You must show use of the $1\mathrm{.}5$IQR rule! Once you demonstrate that an outlier exists, give the individual's ID# and data as your answer below to this question #$1.$ FINALLY, copy the entire data set to the designated region at the right $($several columns over on this worksheet$)$ making sure to delete that one row of data as you copy over so this individual's data will NOT be used in any other calculations performed in answering questions in #$2$ and #$3$ below. You should be left with $70$ rows of data in the region to the right when finished with this problem.

For this problem, we will first assume the data is population data. Now we focus only on the Number in Family variable in the data set you copied to the right...in which you deleted the entire row chosen in answering #$1.$ Again your data table should contain $70$ individuals$$ data. Defining the random variable X to be "Number in Family", complete the following for these seventy data values:

a$.$ What makes X a discrete random variable and not a continuous one?

In the area to the right, create a probability distribution table showing the possible values of X$,$ the frequency of each value, and the associated relative frequency values P$($X$)$ as determined by the collected data.

Determine the expected value $($mean$)$ of the random variable X using your probability distribution table created in part b$.$ directly above. $($Hint: the requirement is to use only the information in the table you produced in part b$.,$ not to use the raw data$---$see how to produce the mean from a probability distribution table via the viation of the random variable X$,$ again using only the values within your probability distribution table. $($You can check your answers by finding the population s$.$d$.$ of the data on family size, BUT this problem needs to be answered through use of only the probability distribution table built in part b$-$ data values $($again take the cleaned data set of $70$ values$)$ and then sort them in order from least to greatest. From this column of Armspan values, create an appropriate frequency table with exactly $7$ classes