b)
The graphical representation of quarterly growth rates of real
b)

Explanation of Solution
The data of quarterly growth rates of real GDP from 1960 to last year using the percent change from a year ago is as follows:
Date | GDP, percentage change from quarter one year ago. |
1960-01-01 | 4.9 |
1960-04-01 | 2.1 |
1960-07-01 | 2.5 |
1960-10-01 | 0.9 |
1961-01-01 | -0.7 |
1961-04-01 | 1.6 |
1961-07-01 | 3.0 |
1961-10-01 | 6.4 |
1962-01-01 | 7.6 |
1962-04-01 | 6.7 |
1962-07-01 | 6.0 |
1962-10-01 | 4.3 |
1963-01-01 | 3.6 |
1963-04-01 | 3.8 |
1963-07-01 | 4.8 |
1963-10-01 | 5.2 |
1964-01-01 | 6.2 |
1964-04-01 | 6.2 |
1964-07-01 | 5.5 |
1964-10-01 | 5.2 |
1965-01-01 | 5.5 |
1965-04-01 | 5.7 |
1965-07-01 | 6.3 |
1965-10-01 | 8.5 |
1966-01-01 | 8.5 |
1966-04-01 | 7.5 |
1966-07-01 | 6.0 |
1966-10-01 | 4.5 |
1967-01-01 | 2.9 |
1967-04-01 | 2.6 |
1967-07-01 | 2.7 |
1967-10-01 | 2.7 |
1968-01-01 | 3.8 |
1968-04-01 | 5.5 |
1968-07-01 | 5.3 |
1968-10-01 | 5.0 |
1969-01-01 | 4.5 |
1969-04-01 | 3.1 |
1969-07-01 | 3.0 |
1969-10-01 | 2.0 |
1970-01-01 | 0.3 |
1970-04-01 | 0.2 |
1970-07-01 | 0.4 |
1970-10-01 | -0.2 |
1971-01-01 | 2.7 |
1971-04-01 | 3.1 |
1971-07-01 | 3.0 |
1971-10-01 | 4.4 |
1972-01-01 | 3.5 |
1972-04-01 | 5.3 |
1972-07-01 | 5.4 |
1972-10-01 | 6.9 |
1973-01-01 | 7.6 |
1973-04-01 | 6.3 |
1973-07-01 | 4.8 |
1973-10-01 | 4.0 |
1974-01-01 | 0.6 |
1974-04-01 | -0.2 |
1974-07-01 | -0.6 |
1974-10-01 | -1.9 |
1975-01-01 | -2.3 |
1975-04-01 | -1.8 |
1975-07-01 | 0.8 |
1975-10-01 | 2.6 |
1976-01-01 | 6.2 |
1976-04-01 | 6.2 |
1976-07-01 | 5.0 |
1976-10-01 | 4.3 |
1977-01-01 | 3.2 |
1977-04-01 | 4.5 |
1977-07-01 | 5.8 |
1977-10-01 | 5.0 |
1978-01-01 | 4.1 |
1978-04-01 | 6.1 |
1978-07-01 | 5.2 |
1978-10-01 | 6.7 |
1979-01-01 | 6.5 |
1979-04-01 | 2.7 |
1979-07-01 | 2.4 |
1979-10-01 | 1.3 |
1980-01-01 | 1.4 |
1980-04-01 | -0.8 |
1980-07-01 | -1.6 |
1980-10-01 | 0.0 |
1981-01-01 | 1.6 |
1981-04-01 | 3.0 |
1981-07-01 | 4.3 |
1981-10-01 | 1.3 |
1982-01-01 | -2.2 |
1982-04-01 | -1.0 |
1982-07-01 | -2.6 |
1982-10-01 | -1.4 |
1983-01-01 | 1.4 |
1983-04-01 | 3.3 |
1983-07-01 | 5.7 |
1983-10-01 | 7.9 |
1984-01-01 | 8.6 |
1984-04-01 | 8.0 |
1984-07-01 | 6.9 |
1984-10-01 | 5.6 |
1985-01-01 | 4.6 |
1985-04-01 | 3.7 |
1985-07-01 | 4.3 |
1985-10-01 | 4.2 |
1986-01-01 | 4.1 |
1986-04-01 | 3.7 |
1986-07-01 | 3.1 |
1986-10-01 | 2.9 |
1987-01-01 | 2.7 |
1987-04-01 | 3.4 |
1987-07-01 | 3.3 |
1987-10-01 | 4.5 |
1988-01-01 | 4.2 |
1988-04-01 | 4.5 |
1988-07-01 | 4.2 |
1988-10-01 | 3.8 |
1989-01-01 | 4.3 |
1989-04-01 | 3.7 |
1989-07-01 | 3.9 |
1989-10-01 | 2.7 |
1990-01-01 | 2.8 |
1990-04-01 | 2.4 |
1990-07-01 | 1.7 |
1990-10-01 | 0.6 |
1991-01-01 | -1.0 |
1991-04-01 | -0.5 |
1991-07-01 | -0.1 |
1991-10-01 | 1.2 |
1992-01-01 | 2.9 |
1992-04-01 | 3.2 |
1992-07-01 | 3.7 |
1992-10-01 | 4.4 |
1993-01-01 | 3.3 |
1993-04-01 | 2.8 |
1993-07-01 | 2.3 |
1993-10-01 | 2.6 |
1994-01-01 | 3.4 |
1994-04-01 | 4.2 |
1994-07-01 | 4.3 |
1994-10-01 | 4.1 |
1995-01-01 | 3.5 |
1995-04-01 | 2.4 |
1995-07-01 | 2.7 |
1995-10-01 | 2.2 |
1996-01-01 | 2.6 |
1996-04-01 | 4.0 |
1996-07-01 | 4.1 |
1996-10-01 | 4.4 |
1997-01-01 | 4.3 |
1997-04-01 | 4.3 |
1997-07-01 | 4.7 |
1997-10-01 | 4.5 |
1998-01-01 | 4.9 |
1998-04-01 | 4.1 |
1998-07-01 | 4.1 |
1998-10-01 | 4.9 |
1999-01-01 | 4.8 |
1999-04-01 | 4.7 |
1999-07-01 | 4.7 |
1999-10-01 | 4.8 |
2000-01-01 | 4.2 |
2000-04-01 | 5.3 |
2000-07-01 | 4.1 |
2000-10-01 | 3.0 |
2001-01-01 | 2.3 |
2001-04-01 | 1.1 |
2001-07-01 | 0.5 |
2001-10-01 | 0.2 |
2002-01-01 | 1.3 |
2002-04-01 | 1.3 |
2002-07-01 | 2.2 |
2002-10-01 | 2.1 |
2003-01-01 | 1.8 |
2003-04-01 | 2.0 |
2003-07-01 | 3.3 |
2003-10-01 | 4.3 |
2004-01-01 | 4.3 |
2004-04-01 | 4.2 |
2004-07-01 | 3.4 |
2004-10-01 | 3.3 |
2005-01-01 | 3.9 |
2005-04-01 | 3.6 |
2005-07-01 | 3.5 |
2005-10-01 | 3.1 |
2006-01-01 | 3.4 |
2006-04-01 | 3.1 |
2006-07-01 | 2.4 |
2006-10-01 | 2.6 |
2007-01-01 | 1.5 |
2007-04-01 | 1.8 |
2007-07-01 | 2.2 |
2007-10-01 | 2.0 |
2008-01-01 | 1.1 |
2008-04-01 | 1.1 |
2008-07-01 | 0.0 |
2008-10-01 | -2.8 |
2009-01-01 | -3.3 |
2009-04-01 | -3.9 |
2009-07-01 | -3.0 |
2009-10-01 | 0.2 |
2010-01-01 | 1.7 |
2010-04-01 | 2.8 |
2010-07-01 | 3.2 |
2010-10-01 | 2.6 |
2011-01-01 | 1.9 |
2011-04-01 | 1.7 |
2011-07-01 | 0.9 |
2011-10-01 | 1.6 |
2012-01-01 | 2.7 |
2012-04-01 | 2.4 |
2012-07-01 | 2.5 |
2012-10-01 | 1.5 |
2013-01-01 | 1.6 |
2013-04-01 | 1.3 |
2013-07-01 | 1.9 |
2013-10-01 | 2.6 |
2014-01-01 | 1.4 |
2014-04-01 | 2.7 |
2014-07-01 | 3.1 |
2014-10-01 | 2.9 |
2015-01-01 | 4.0 |
2015-04-01 | 3.3 |
2015-07-01 | 2.4 |
2015-10-01 | 1.9 |
2016-01-01 | 1.6 |
2016-04-01 | 1.3 |
2016-07-01 | 1.6 |
2016-10-01 | 2.0 |
2017-01-01 | 2.1 |
2017-04-01 | 2.2 |
2017-07-01 | 2.4 |
2017-10-01 | 2.8 |
2018-01-01 | 2.9 |
c)
The graphical representation of quarterly growth rates of real GDP from 1960 to last year using the percent change from preceding period quarterly. To ascertain the least volatile and most volatile measure, and the differences between these three series.
c)

Explanation of Solution
The data of quarterly growth rates of real GDP from 1960 to last year using the percent change from preceding period quarterly is as follows:
Date | GDP percent change from preceding period, quarterly |
1960-04-01 | -2.1 |
1960-07-01 | 2.0 |
1960-10-01 | -5.0 |
1961-01-01 | 2.7 |
1961-04-01 | 7.0 |
1961-07-01 | 7.9 |
1961-10-01 | 8.1 |
1962-01-01 | 7.3 |
1962-04-01 | 3.7 |
1962-07-01 | 5.0 |
1962-10-01 | 1.3 |
1963-01-01 | 4.4 |
1963-04-01 | 4.6 |
1963-07-01 | 9.1 |
1963-10-01 | 2.6 |
1964-01-01 | 8.7 |
1964-04-01 | 4.4 |
1964-07-01 | 6.4 |
1964-10-01 | 1.2 |
1965-01-01 | 10.0 |
1965-04-01 | 5.1 |
1965-07-01 | 9.2 |
1965-10-01 | 9.5 |
1966-01-01 | 10.1 |
1966-04-01 | 1.4 |
1966-07-01 | 3.4 |
1966-10-01 | 3.3 |
1967-01-01 | 3.6 |
1967-04-01 | 0.2 |
1967-07-01 | 3.8 |
1967-10-01 | 3.0 |
1968-01-01 | 8.4 |
1968-04-01 | 6.9 |
1968-07-01 | 3.1 |
1968-10-01 | 1.6 |
1969-01-01 | 6.4 |
1969-04-01 | 1.2 |
1969-07-01 | 2.7 |
1969-10-01 | -1.9 |
1970-01-01 | -0.6 |
1970-04-01 | 0.6 |
1970-07-01 | 3.7 |
1970-10-01 | -4.2 |
1971-01-01 | 11.3 |
1971-04-01 | 2.2 |
1971-07-01 | 3.3 |
1971-10-01 | 0.9 |
1972-01-01 | 7.6 |
1972-04-01 | 9.4 |
1972-07-01 | 3.8 |
1972-10-01 | 6.9 |
1973-01-01 | 10.3 |
1973-04-01 | 4.4 |
1973-07-01 | -2.1 |
1973-10-01 | 3.8 |
1974-01-01 | -3.4 |
1974-04-01 | 1.0 |
1974-07-01 | -3.7 |
1974-10-01 | -1.5 |
1975-01-01 | -4.8 |
1975-04-01 | 2.9 |
1975-07-01 | 7.0 |
1975-10-01 | 5.5 |
1976-01-01 | 9.3 |
1976-04-01 | 3.0 |
1976-07-01 | 2.2 |
1976-10-01 | 2.9 |
1977-01-01 | 4.8 |
1977-04-01 | 8.0 |
1977-07-01 | 7.4 |
1977-10-01 | 0.0 |
1978-01-01 | 1.3 |
1978-04-01 | 16.4 |
1978-07-01 | 4.1 |
1978-10-01 | 5.5 |
1979-01-01 | 0.7 |
1979-04-01 | 0.4 |
1979-07-01 | 3.0 |
1979-10-01 | 1.0 |
1980-01-01 | 1.3 |
1980-04-01 | -8.0 |
1980-07-01 | -0.5 |
1980-10-01 | 7.7 |
1981-01-01 | 8.1 |
1981-04-01 | -2.9 |
1981-07-01 | 4.9 |
1981-10-01 | -4.3 |
1982-01-01 | -6.1 |
1982-04-01 | 1.8 |
1982-07-01 | -1.5 |
1982-10-01 | 0.2 |
1983-01-01 | 5.4 |
1983-04-01 | 9.4 |
1983-07-01 | 8.2 |
1983-10-01 | 8.6 |
1984-01-01 | 8.1 |
1984-04-01 | 7.1 |
1984-07-01 | 3.9 |
1984-10-01 | 3.3 |
1985-01-01 | 3.9 |
1985-04-01 | 3.6 |
1985-07-01 | 6.2 |
1985-10-01 | 3.0 |
1986-01-01 | 3.8 |
1986-04-01 | 1.8 |
1986-07-01 | 3.9 |
1986-10-01 | 2.2 |
1987-01-01 | 3.0 |
1987-04-01 | 4.4 |
1987-07-01 | 3.5 |
1987-10-01 | 7.0 |
1988-01-01 | 2.1 |
1988-04-01 | 5.4 |
1988-07-01 | 2.4 |
1988-10-01 | 5.4 |
1989-01-01 | 4.1 |
1989-04-01 | 3.1 |
1989-07-01 | 3.0 |
1989-10-01 | 0.8 |
1990-01-01 | 4.4 |
1990-04-01 | 1.5 |
1990-07-01 | 0.3 |
1990-10-01 | -3.6 |
1991-01-01 | -1.9 |
1991-04-01 | 3.2 |
1991-07-01 | 2.0 |
1991-10-01 | 1.4 |
1992-01-01 | 4.9 |
1992-04-01 | 4.4 |
1992-07-01 | 4.0 |
1992-10-01 | 4.2 |
1993-01-01 | 0.7 |
1993-04-01 | 2.3 |
1993-07-01 | 1.9 |
1993-10-01 | 5.6 |
1994-01-01 | 3.9 |
1994-04-01 | 5.5 |
1994-07-01 | 2.4 |
1994-10-01 | 4.7 |
1995-01-01 | 1.4 |
1995-04-01 | 1.2 |
1995-07-01 | 3.5 |
1995-10-01 | 2.7 |
1996-01-01 | 3.0 |
1996-04-01 | 6.8 |
1996-07-01 | 3.6 |
1996-10-01 | 4.2 |
1997-01-01 | 2.6 |
1997-04-01 | 6.8 |
1997-07-01 | 5.1 |
1997-10-01 | 3.5 |
1998-01-01 | 4.1 |
1998-04-01 | 3.8 |
1998-07-01 | 5.1 |
1998-10-01 | 6.6 |
1999-01-01 | 3.8 |
1999-04-01 | 3.1 |
1999-07-01 | 5.3 |
1999-10-01 | 7.0 |
2000-01-01 | 1.5 |
2000-04-01 | 7.5 |
2000-07-01 | 0.5 |
2000-10-01 | 2.5 |
2001-01-01 | -1.1 |
2001-04-01 | 2.4 |
2001-07-01 | -1.7 |
2001-10-01 | 1.1 |
2002-01-01 | 3.5 |
2002-04-01 | 2.4 |
2002-07-01 | 1.8 |
2002-10-01 | 0.6 |
2003-01-01 | 2.2 |
2003-04-01 | 3.5 |
2003-07-01 | 7.0 |
2003-10-01 | 4.7 |
2004-01-01 | 2.2 |
2004-04-01 | 3.1 |
2004-07-01 | 3.8 |
2004-10-01 | 4.1 |
2005-01-01 | 4.5 |
2005-04-01 | 1.9 |
2005-07-01 | 3.6 |
2005-10-01 | 2.6 |
2006-01-01 | 5.4 |
2006-04-01 | 0.9 |
2006-07-01 | 0.6 |
2006-10-01 | 3.5 |
2007-01-01 | 0.9 |
2007-04-01 | 2.3 |
2007-07-01 | 2.2 |
2007-10-01 | 2.5 |
2008-01-01 | -2.3 |
2008-04-01 | 2.1 |
2008-07-01 | -2.1 |
2008-10-01 | -8.4 |
2009-01-01 | -4.4 |
2009-04-01 | -0.6 |
2009-07-01 | 1.5 |
2009-10-01 | 4.5 |
2010-01-01 | 1.5 |
2010-04-01 | 3.7 |
2010-07-01 | 3.0 |
2010-10-01 | 2.0 |
2011-01-01 | -1.0 |
2011-04-01 | 2.9 |
2011-07-01 | -0.1 |
2011-10-01 | 4.7 |
2012-01-01 | 3.2 |
2012-04-01 | 1.7 |
2012-07-01 | 0.5 |
2012-10-01 | 0.5 |
2013-01-01 | 3.6 |
2013-04-01 | 0.5 |
2013-07-01 | 3.2 |
2013-10-01 | 3.2 |
2014-01-01 | -1.1 |
2014-04-01 | 5.5 |
2014-07-01 | 5.0 |
2014-10-01 | 2.3 |
2015-01-01 | 3.2 |
2015-04-01 | 3.0 |
2015-07-01 | 1.3 |
2015-10-01 | 0.1 |
2016-01-01 | 2.0 |
2016-04-01 | 1.9 |
2016-07-01 | 2.2 |
2016-10-01 | 2.0 |
2017-01-01 | 2.3 |
2017-04-01 | 2.2 |
2017-07-01 | 3.2 |
2017-10-01 | 3.5 |
2018-01-01 | 2.5 |
2018-04-01 | 3.5 |
The graphical representation of the quarterly growth rates of real GDP from 1960 to 2018 using the percent change from the previous quarter is as follows:
The quarterly percent change at the annual rate indicates the percent change, if the quarterly rate goes on for four quarters. It is calculated by compounding of quarterly rate for four quarters.
For some unpredictable quarterly series, percentage changes at quarterly rates rather than at annual rates are preferred because the question of comparability is less relevant and because the annual rate of change is smaller.
When these three data and their respective graph compare to each other for some specific successive period of time, following result is determined:
- 2nd one that is, GDP growth rate using percentage change from quarter one year ago is most volatile and 3rd way that is, GDP growth rate by using percent change from preceding period quarterly is least volatile.
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