MS 150 Statistics summer 2007 Mx • Name:

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 µ 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 µ 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

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.

19. __________ Calculate the slope of the linear trend line for the data.
20. __________ Calculate the y-intercept for the data.
21. __________ Is the correlation positive, negative, or neutral?
22. __________ Determine the correlation coefficient r.
23. __________ Is the correlation none, low, moderate, high, or perfect?
24. __________ Does the relationship appear to be linear or non-linear?
25. __________ What is the projected power consumption a year from now in month number 41?
26. __________ What month number had a power consumption of 25918 KwH?

Table of statistical functions used by OpenOffice

Statistic or Parameter	Symbol	Equations	OpenOffice
Square root			=SQRT(number)
Sample mean	x	Σx/n	=AVERAGE(data)
Sample standard deviation	sx		=STDEV(data)
Sample Coefficient of Variation	CV	sx/ x	=STDEV(data)/AVERAGE(data)
Calculate a z value from an x	z	=	=STANDARDIZE(x;μ;σ)
Slope	b		=SLOPE(y data;x data)
Intercept	a		=INTERCEPT(y data;x data)
Correlation	r		=CORREL(y data;x data)