Question

Sharpe Middle School is applying for a grant that will be used to add fitness equipment to the gym. The principal surveyed 16 anonymous students to determine how many minutes a day the students spend exercising. The results from the 16 anonymous students are shown.

0 minutes; 40 minutes; 60 minutes; 30 minutes; 60 minutes; 10 minutes; 45 minutes; 30 minutes; 300 minutes; 90 minutes; 30 minutes; 120 minutes; 60 minutes; 60 minutes; 0 minutes; 20 minutes

** Lp = (p/100) (n + 1) (the p-th percentile formula to get the location).

Determine the following five values.

Min =

Q1 =

Med =

Q3 =

Max =

If you were the principal, would you be justified in purchasing new fitness equipment?  

ANSWER:

Is/are there any potential outlier (s)?

IQR=Q3-Q1=………………………………

Lower Limit: Q1 - 1.5(IQR) =……-…………..

Upper Limit: Q3 + 1.5(IQR)=……………..

Calculating the Arithmetic Mean of Grouped Frequency Tables

When only grouped data is available, you do not know the individual data values (we only know intervals and interval frequencies); therefore, you cannot compute an exact mean for the data set. What we must do is estimate the actual mean by calculating the mean of a frequency table. A frequency table is a data representation in which grouped data is displayed along with the corresponding frequencies. To calculate the mean from a grouped frequency table we can apply the basic definition of mean: mean = data sum/number of data values.

We simply need to modify the definition to fit within the restrictions of a frequency table.

Since we do not know the individual data values we can instead find the midpoint of each interval.  

The midpoint is = (lower boundary + upper boundary)/2.

We can now modify the mean definition to be  

                   Mean of Frequency Table = Σ f m/Σ f

where f = the frequency of the interval and m = the midpoint of the interval.

Answer 1