Question

9 of 28 (27 complete) Score: 3 of 7 pts 8.A.31 The table shows the number of monthly active users of a social media website (the number of people who use the website at least once a month) over a three-year pero Month March 2009 March 2010 March 2011 March 2012 Monthly active users (millions) 182 425 654 Absolute change over previous year Percent change over previous year Monthly active users (millions) 182 Absolute change over previous year Type integers or decimals rounded to the nearest tenth as needed.) b. Fill in the row of the table showing the percent change in the number of active monthly users Month March 2009 March 2010 March 2011 March 2012 Monthly active users (millions) 182 Percent change over previous % year Type integers or decimals rounded to the nearest tenth as needed) Enter your answer in the edit fields and then click Check Answer 1 part I remaining

Answer 1

Month	March 2009	March 2010	March 2011	March 2012
Monthly active users (millions)	182	425	654	890
Absolute change over previous year (millions)	-
Percentage change over previous year (%)	-

The problem gives data on monthly active users of a social media website over a three-year period. By active users here we mean users who use the website at least once a month. We have to find the absolute change over the previous year and percentage change over the previous year for the years 2010, 2011 and 2012, since there is no data available for 2008, i.e., the year before 2009.

Absolute change refers to change occurring between two observations, regardless of the direction of change,i.e., the simple difference between two observations on a similar event. E.g. if V₁ and V₂ are the marks obtained by a student in mathematics in Unit Test-I and Unit Test-II respectively, the absolute change in her/his marks is |V₁-V₂|.

• There were 182=V₁(say) users active in March 2009 and 425=V₂(say) users active in March 2010. The simple difference between the two observations,i.e., the number of users active in 2009 and in 2010 is |V₁-V₂| =425-182 =243.
• There were 425=V₁(say) users active in March 2010 and 654=V₂(say) users active in March 2011. The simple difference between the two observations,i.e., the number of users active in 2010 and in 2011 is |V₁-V₂| =654-425 =229.
• There were 654=V₁(say) users active in March 2011 and 890=V₂(say) users active in March 2012. The simple difference between the two observations,i.e., the number of users active in 2011 and in 2012 is |V₁-V₂| =890-654 =236.

The simple difference over a year itself is the absolute change over that year. Thus, the above table takes the form:

Month	March 2009	March 2010	March 2011	March 2012
Monthly active users (millions)	182	425	654	890
Absolute change over previous year (millions)	-	243	229	236
Percentage change over previous year (%)	-

Percentage change refers to the percentage of the difference between the observations on the absolute value of the former, or previous observation. The percentage can refer to increase or decrease. If the latter observation is greater than the previous observation, the result is called percentage increase. If the latter observation is less than the previous observation,the result is called percentage decrease. E.g. if V₁ and V₂ are the marks obtained by a student in mathematics in Unit Test-I and Unit Test-II respectively, the percentage change in her/his marks is

• |(V₁-V₂)/V₁|% increase, if V₁<V₂.
• |(V₁-V₂)/V₁|% decrease, if V₁>V₂.

Now,

• There were 182=V₁(say) users active in March 2009 and 425=V₂(say) users active in March 2010. The difference between the two observations,i.e., the number of users active in 2009 and in 2010 is |V₁-V₂|=425-182=243. Here, V₁<V₂. So, for the year 2010, there has been |(V₁-V₂)/V₁|% increase =|243/182|% increase =133.52% increase.
• There were 425=V₁(say) users active in March 2010 and 654=V₂(say) users active in March 2011. The difference between the two observations,i.e., the number of users active in 2010 and in 2011 is |V₁-V₂|=654-425=229. Here, V₁<V₂. So, for the year 2011, there has been |(V₁-V₂)/V₁|% increase =|229/425|% increase =53.88% increase.
• There were 654=V₁(say) users active in March 2011 and 890=V₂(say) users active in March 2012. The difference between the two observations,i.e., the number of users active in 2011 and in 2012 is |V₁-V₂|=890-654=236. Here, V₁<V₂. So, for the year 2012, there has been |(V₁-V₂)/V₁|% increase =|236/654|% increase =36.08% increase.

Seeing the above results, the table can now be written as:

Month	March 2009	March 2010	March 2011	March 2012
Monthly active users (millions)	182	425	654	890
Absolute change over previous year (millions)	-	243	229	236
Percentage change over previous year (%)	-	133.52	53.88	36.08