### MS 150 Statistics fall 2005 Test One • Name:

LRC kwh
15400
25500
26400
27100
31500
24400
34600
28100
29100
26700
47900
31300

#### II. Basic statistics and histogram

Use the Learning Resource Center (LRC) kilowatt hour (kwh) data for this section. The data is the monthly power consumption for the LRC for twelve months between June 2004 to July 2005.

1. __________ Find the sample size n for the power data.
2. __________ Find the minimum power.
3. __________ Find the maximum power.
4. __________ Find the range of the power.
5. __________ Find the median power.
6. __________ Find the mode for the power.
7. __________ Find the sample mean power.
8. __________ Find the sample standard deviation for the power.
9. __________ Find the sample coefficient of variation CV.
10. __________ If this data is to be divided into five bins, what is the width of a single bin?
11. Determine the frequency and calculate the relative frequency using five bins (classes, intervals). Record your results in the table provided.
BinsFrequencyRelative Frequency

Sums:
12. Sketch a frequency histogram of the data, labeling your horizontal axis and vertical axis as appropriate. Use the back of this sheet if necessary.

The following data is the net power consumption for the LRC in spring 2003, spring 2004, and spring 2005. Use this data to find the linear regression (trend line) for this data.

Spring term (x)Net kwh (y)
0397200
04118000
05118500
1. ______________ Calculate the slope of the linear regression (trend line) for the data.
2. ______________ Calculate the y-intercept of the linear regression (trend line) for the data.
3. ______________ Is the correlation positive or negative?
4. ______________ Use the slope and intercept to calculate the projected power usage in spring 06. Go ahead and make this projection even though '06 is beyond the data provided.
5. ______________ Use the slope and intercept to calculate the projected year in which power usage is 144,000 kwh. Go ahead and make this projection even though 144000 is beyond the data provided.
Table of statistical functions used by Excel
Basic Statistics
Statistic or ParameterSymbolEquationsExcel
Sample sizen=COUNT(data)
Minimum=MIN(data)
Maximum=MAX(data)
Median=MEDIAN(data)
Mode=MODE(data)
Sample meanx Σx/n=AVERAGE(data)
Sample standard deviationsx=STDEV(data)
Sample Coefficient of VariationCV sx/x =STDEV(data)/AVERAGE(data)
Linear Regression Statistics
Statistic or ParameterSymbolEquationsExcel
Slopeb=SLOPE(y data, x data)
Intercepta=INTERCEPT(y data, x data)
Correlationr=CORREL(y data, x data)
Coefficient of Determinationr2 =(CORREL(y data, x data))^2