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.
- __________ What level of measurement is the data?
- __________ Find the sample size n for the data.
- __________ Find the minimum.
- __________ Find the maximum.
- __________ Find the range.
- __________ Find the median.
- __________ Find the mode.
- __________ Find the sample mean x.
- __________ Find the sample standard deviation sx.
- __________ Find the sample coefficient of variation CV.
- __________ If this data were to be divided into four bins, what would be the width of a single bin?
- Determine the frequency and calculate the relative frequency using four bins. Record your results in the table provided.
|Bins (x)||Frequency (f)||Rel. Freq. p(x)|
- Sketch a frequency histogram chart of the data here or on the back, labeling your horizontal axis and vertical axis as appropriate.
- ____________________ What is the shape of the distribution?
- ____________________ Use the mean ” and standard deviation σ calculated above to determine the z-score for the 2.92 minute lap.
- ____________________ Does the 2.92 minute lap have an ordinary or unusual z-score?
- ____________________ Bearing in mind that higher lap times are slower laps and slower speeds. Was my speed unusually low as measured by z-score?
- ____________________ 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
|Month||Month number (x)||Power/KwH (y)|
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.
- __________ Calculate the slope of the linear trend line for the data.
- __________ Calculate the y-intercept for the data.
- __________ Is the correlation positive, negative, or neutral?
- __________ Determine the correlation coefficient r.
- __________ Is the correlation none, low, moderate, high, or perfect?
- __________ Does the relationship appear to be linear or non-linear?
- __________ What is the projected power consumption a year from now in month number 41?
- __________ What month number had a power consumption of 25918 KwH?
Table of statistical functions used by OpenOffice
|Statistic or Parameter||Symbol||Equations||OpenOffice|
|Sample standard deviation||sx||=STDEV(data)|
|Sample Coefficient of Variation||CV||sx/
|Calculate a z value from an x||z||=
|Slope||b||=SLOPE(y data;x data)|
|Intercept||a||=INTERCEPT(y data;x data)|
|Correlation||r||=CORREL(y data;x data)|