Mean, Variance, Median, Quartiles The STAT command computes descriptive statistics on variables. Example A data set is available with inflation rates for five industrial countries. Which country's inflation rate is the most volatile ? Higher volatility is associated with higher variance. The SHAZAM commands (filename: IRATE.SHA) below can be used to answer the question. SAMPLE 1 21 READ (IRATE.txt) YEAR USA UK JAPAN GERMANY FRANCE STAT USA UK JAPAN GERMANY FRANCE / PMEDIAN STOP The STAT command computes the mean, variance, standard deviation, minimum and maximum for each variable in the variable list. The PMEDIAN option requests for calculation of the median, mode, quartiles and interquartile range for each variable. The SHAZAM output can be viewed. The results show that the inflation rate of the United Kingdom is the most variable with a standard deviation of 6.3. The least variable rate is Germany's inflation rate with a standard deviation of 1.7. (Note that the numerical results have been rounded to 1 decimal place. The SHAZAM output typically reports more digits than are needed for report presentation.) An equivalent way of preparing the above command file is to assign variable names C1, C2, C3, C4 and C5 for the inflation rates in the 5 countries. This notation saves typing effort. SHAZAM commands that do the same work as above are: SAMPLE 1 21 READ (IRATE.txt) YEAR C1-C5 STAT C1-C5 / PMEDIAN STOP   Changing the Sample Period The world economy was affected by the Middle East War of October 1973 that was followed by an Arab oil embargo with a subsequent quadrupling in international oil prices. The SHAZAM commands that follow investigate differences in inflation rates for the pre-embargo and post-embargo period. Descriptive statistics are obtained for the two sample periods 1960 to 1973 and 1974 to 1980. SAMPLE 1 21 READ (IRATE.txt) YEAR USA UK JAPAN GERMANY FRANCE * Sample period 1960 to 1973 SAMPLE 1 14 STAT USA UK JAPAN GERMANY FRANCE * Sample period 1974 to 1980 SAMPLE 15 21 STAT USA UK JAPAN GERMANY FRANCE STOP The above commands demonstrate that the SAMPLE command is an important and useful command. The SAMPLE command is typically the first command in a SHAZAM program. The sample period can be changed by specifying a new SAMPLE command. The SHAZAM output can be viewed. [SHAZAM Guide home] SHAZAM output |_SAMPLE 1 21 |_READ (IRATE.txt) YEAR USA UK JAPAN GERMANY FRANCE UNIT 88 IS NOW ASSIGNED TO: IRATE.txt 6 VARIABLES AND 21 OBSERVATIONS STARTING AT OBS 1 |_STAT USA UK JAPAN GERMANY FRANCE / PMEDIAN NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM USA 21 5.1238 3.6950 13.653 1.1000 13.600 UK 21 8.5476 6.3210 39.956 1.0000 24.200 JAPAN 21 7.3476 4.6330 21.465 3.6000 24.600 GERMANY 21 3.8667 1.6764 2.8103 1.5000 7.0000 FRANCE 21 6.7143 3.5791 12.810 2.6000 14.000 VARIABLE = USA MEDIAN = 4.3000 LOWER 25%= 1.5500 UPPER 25%= 7.0000 INTERQUARTILE RANGE= 5.450 MODE = 2.8000 WITH 2 OBSERVATIONS WARNING: MULTIPLE MODES - THE MAXIMUM IS REPORTED VARIABLE = UK MEDIAN = 6.5000 LOWER 25%= 3.8000 UPPER 25%= 14.650 INTERQUARTILE RANGE= 10.85 MODE NOT APPLICABLE VARIABLE = JAPAN MEDIAN = 6.3000 LOWER 25%= 4.4500 UPPER 25%= 8.0500 INTERQUARTILE RANGE= 3.600 MODE = 3.6000 WITH 2 OBSERVATIONS VARIABLE = GERMANY MEDIAN = 3.7000 LOWER 25%= 2.3000 UPPER 25%= 5.3500 INTERQUARTILE RANGE= 3.050 MODE = 7.0000 WITH 2 OBSERVATIONS WARNING: MULTIPLE MODES - THE MAXIMUM IS REPORTED VARIABLE = FRANCE MEDIAN = 5.5000 LOWER 25%= 3.4000 UPPER 25%= 9.5000 INTERQUARTILE RANGE= 6.100 MODE = 5.5000 WITH 2 OBSERVATIONS WARNING: MULTIPLE MODES - THE MAXIMUM IS REPORTED |_STOP [Back to Top] [SHAZAM Guide home] SHAZAM output |_SAMPLE 1 21 |_READ (IRATE.txt) YEAR USA UK JAPAN GERMANY FRANCE UNIT 88 IS NOW ASSIGNED TO: IRATE.txt 6 VARIABLES AND 21 OBSERVATIONS STARTING AT OBS 1 |_* Sample period 1960 to 1973 |_SAMPLE 1 14 |_STAT USA UK JAPAN GERMANY FRANCE NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM USA 14 3.0500 1.8275 3.3396 1.1000 6.2000 UK 14 4.8000 2.3485 5.5154 1.0000 9.5000 JAPAN 14 6.0857 2.1300 4.5367 3.6000 12.000 GERMANY 14 3.4143 1.6379 2.6829 1.5000 7.0000 FRANCE 14 4.5143 1.5195 2.3090 2.6000 7.5000 |_* Sample period 1974 to 1980 |_SAMPLE 15 21 |_STAT USA UK JAPAN GERMANY FRANCE NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM USA 7 9.2714 2.8582 8.1690 5.8000 13.600 UK 7 16.043 4.7878 22.923 8.3000 24.200 JAPAN 7 9.8714 7.1114 50.572 3.6000 24.600 GERMANY 7 4.7714 1.4568 2.1224 2.7000 7.0000 FRANCE 7 11.114 1.9540 3.8181 9.1000 14.000 |_STOP [Back to Top] [SHAZAM Guide home]