### MS 150 Statistics summer 2007 Mx • Name:

Joggling
time/min
2.77
2.86
2.86
2.81
2.81
2.82
2.82
2.80
2.88
2.91
2.88
2.92
2.67
2.76
2.69
2.64
2.66

#### Part I: Basic statistics, frequencies, histogram, z-scores, normal distribution.

Last night I went out and ran a midsummer's night seventeen joggling laps at the track. I timed each lap. Use my lap times for this first part of the test.

1. __________ What level of measurement is the data?
2. __________ Find the sample size n for the data.
3. __________ Find the minimum.
4. __________ Find the maximum.
5. __________ Find the range.
6. __________ Find the median.
7. __________ Find the mode.
8. __________ Find the sample mean x.
9. __________ Find the sample standard deviation sx.
10. __________ Find the sample coefficient of variation CV.
11. __________ If this data were to be divided into four bins, what would be the width of a single bin?
12. Determine the frequency and calculate the relative frequency using four bins. Record your results in the table provided.
Frequency table
Bins (x)Frequency (f)Rel. Freq. p(x)
_____________________
_____________________
_____________________
_____________________
Sum: ______________
13. Sketch a frequency histogram chart of the data here or on the back, labeling your horizontal axis and vertical axis as appropriate.
14. ____________________ What is the shape of the distribution?
15. ____________________ Use the mean ” and standard deviation σ calculated above to determine the z-score for the 2.92 minute lap.
16. ____________________ Does the 2.92 minute lap have an ordinary or unusual z-score?
17. ____________________ Bearing in mind that higher lap times are slower laps and slower speeds. Was my speed unusually low as measured by z-score?
18. ____________________ Use the mean ” and standard deviation σ calculated above to determine the lap time which would have a z-score equal to negative two. Any lap time less than this value would be an unusually fast lap (low times are fast laps).

#### Part II: Linear regression

LRC: Building H
MonthMonth number (x)Power/KwH (y)
Oct 061024100
Nov 061126800
Dec 061226300
Jan 071320400
Feb 071426000
Mar 071517500
Apr 071627700
May 071723400

On Thursday maintenance released their semi-annual energy audit spreadsheet. The building that uses the most power is the Learning Resource Center. The table provides power consumption data in kilowatt-hours (KwH). For comparison purposes, my own home uses about 290 KwH per month.

1. __________ Calculate the slope of the linear trend line for the data.
2. __________ Calculate the y-intercept for the data.
3. __________ Is the correlation positive, negative, or neutral?
4. __________ Determine the correlation coefficient r.
5. __________ Is the correlation none, low, moderate, high, or perfect?
6. __________ Does the relationship appear to be linear or non-linear?
7. __________ What is the projected power consumption a year from now in month number 41?
8. __________ What month number had a power consumption of 25918 KwH?
Table of statistical functions used by OpenOffice
Statistic or ParameterSymbolEquationsOpenOffice
Square root=SQRT(number)
Sample meanx Σx/n =AVERAGE(data)
Sample standard deviationsx=STDEV(data)
Sample Coefficient of VariationCVsx/ x =STDEV(data)/AVERAGE(data)
Calculate a z value from an xz= =STANDARDIZE(x;μ;σ)
Slopeb=SLOPE(y data;x data)
Intercepta=INTERCEPT(y data;x data)
Correlationr=CORREL(y data;x data)