## Out for a run!

#### Basic statistics

On Wednesday evening I jogged home from the College. As I jogged I kept track of my time as I passed various points at known distances. When I got home I checked my pace on each leg of the jog. The following table records my pace on each leg.

Pace in minutes per km per leg
End pointPace
Mount Dolon6.35
First bridge5.92
Third bridge5.47
Sokehs junction6.92
6-11 Junction7.50
Dolihner8.72
1. __________ Find the sample size n for the pace per leg data.
2. __________ Find the minimum pace.
3. __________ Find the maximum pace.
4. __________ Find the range of the pace.
5. __________ Find the median pace.
6. __________ Find the mode for the pace.
7. __________ Find the sample mean pace.
8. __________ Find the sample standard deviation pace.
9. __________ Find the sample coefficient of variation CV.
10. __________ If this data were to be divided into five bins, what would be the width of a single bin?

#### Frequencies, histograms, and probabilities

1. Lee Ling's paces were calculated for 32 legs and recorded in the table below. Complete this table using the data given in the table. Calculate the relative frequency and the mean pace at which Lee Ling jogs.
Pace Legs
binsFreqRF or P(x)Mean calc
5.383____________________
6.005____________________
6.6314____________________
7.266____________________
7.884____________________
Sums:______________________________

Mean pace at which Lee Ling jogs: _______________
2. Sketch a relative frequency histogram of the data here or on the back, labeling your horizontal axis and vertical axis as appropriate.
3. __________ What is the shape of the distribution?
4. __________ Determine P(x <= 5.38 minutes per kilometer)
5. __________ Determine P(6.00 < x <= 6.63 minutes per kilometer)
6. __________ What is the probability of rolling a four or a six on an eight sided die?

#### Linear relationships and regressions

##### Matching
1. __________ Negative linear relationship
2. __________ Positive linear relationship
3. __________ Non-linear relationship
4. __________ Random, no relationship
##### Linear regression

On the Wednesday evening jog home I logged the following distance versus time data:

Time vs distance Wednesday evening jog
LocationTime/minDist/km
College0.000.0
Mount Dolon20.973.3
First bridge28.674.6
Third bridge34.135.6
Sokehs junction54.908.6
6-11 Junction60.909.4
Dolihner63.529.7
1. __________ Calculate the slope of the linear trend line (also known as best fit line, least squares, linear regression) for the time versus distance data.
2. __________ Calculate the y-intercept for the data.
3. __________ Is the correlation positive, negative, or neutral?
4. __________ Determine the correlation coefficient
5. __________ Is the correlation none, low, moderate, high, or perfect?
6. __________ Determine the coefficient of determination.
7. __________ What percent in the variation in time explains the variation in distance?
8. __________ Based on the equation of the trend line, what would be the predicted distance for a 45 minute jog?
9. __________ Based on the equation of the trend line, what would be the predicted time for a 2 kilometer jog?
10. __________ Based on the equation of the trend line, what would be the time for a 80 kilometer jog?
Statistic or Parameter Symbol Equations Excel
Square root =SQRT(number)
Sample mean x Σx/n =AVERAGE(data)
Sample standard deviation sx =STDEV(data)
Sample Coefficient of Variation CV 100(sx/x =100*STDEV(data)/AVERAGE(data)
Slope b =SLOPE(y data, x data)
Intercept a =INTERCEPT(y data, x data)
Correlation r =CORREL(y data, x data)
Coefficient of Determination =(CORREL(y data, x data))^2

__________ Do you use the textbook?
__________ Do you find the textbook to be helpful?
What would be your comments on changing from using the textbook to having the students purchase bound copies of the class notes from the bookstore for next Fall?