Summary statistics: Column n Mean Std. dev. Median IQR Rainfall (in.) 135 14.98
ID: 3238670 • Letter: S
Question
Summary statistics:
Column
n
Mean
Std. dev.
Median
IQR
Rainfall (in.)
135
14.98
7.03
13.13
9.68
Above is a histogram and summary statistics for the seasonal rainfall data (in inches) in Los Angeles for each season from 1877 to 2012, recorded at the Los Angeles Civic Center. The data are obtained from the Los Angeles Almanac. The rain seasons are on a fiscal year basis (July 1 to June 30). Thus the season 2008-2009 refers to the period July 1, 2008 to June 30, 2009. We are interested in analyzing the seasonal rainfall measurements (in inches). In your post respond to the following:
1) Which is the better summary of the seasonal rainfall in Los Angeles, the mean or the median? Explain.
2) Which is a better summary of the spread, the IQR or the standard deviation? Explain.
3) Based on the Normal Model, about what percentage of seasons should have rainfall within one standard deviation of the mean?
4) Look at the data file attached (see link below) to answer the following: What percentage of seasons actually have rainfall within one standard deviation from the mean?
5) Explain the discrepancy between your answers to #3 and #4.
Seasonal Rainfall data.xlsx
Column
n
Mean
Std. dev.
Median
IQR
Rainfall (in.)
135
14.98
7.03
13.13
9.68
Seasonal Rainfall in Los Angeles (1877 2012) Frequency 45 40 33 30 28 20 14 10 20 10 30 40 Rainfall (inches)Explanation / Answer
Answer:
Summary statistics:
Column
n
Mean
Std. dev.
Median
IQR
Rainfall (in.)
135
14.98
7.03
13.13
9.68
Above is a histogram and summary statistics for the seasonal rainfall data (in inches) in Los Angeles for each season from 1877 to 2012, recorded at the Los Angeles Civic Center. The data are obtained from the Los Angeles Almanac. The rain seasons are on a fiscal year basis (July 1 to June 30). Thus the season 2008-2009 refers to the period July 1, 2008 to June 30, 2009. We are interested in analyzing the seasonal rainfall measurements (in inches). In your post respond to the following:
1) Which is the better summary of the seasonal rainfall in Los Angeles, the mean or the median? Explain.
Since the data is positively skewed, median is better summary.
2) Which is a better summary of the spread, the IQR or the standard deviation? Explain.
Since the data is positively skewed, IQR is better summary.
3) Based on the Normal Model, about what percentage of seasons should have rainfall within one standard deviation of the mean?
68% of seasons should have rainfall within one standard deviation of the mean.
4) Look at the data file attached (see link below) to answer the following: What percentage of seasons actually have rainfall within one standard deviation from the mean?
mean - 1s
7.95
mean + 1s
22.01
percent in interval
74.8%
5) Explain the discrepancy between your answers to #3 and #4.
Since data are not normally distributed, there is discrepancy in the two answers.
Column
n
Mean
Std. dev.
Median
IQR
Rainfall (in.)
135
14.98
7.03
13.13
9.68
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