The Big Bang Theory, a situation comedy featuring Johnney Galecki, Jim Parsons,
ID: 3275258 • Letter: T
Question
The Big Bang Theory, a situation comedy featuring Johnney Galecki, Jim Parsons, and Kaley Cuoco-Sweeting, is one of the most watched programs on network television. The first two episodes for the 2011-2012 season premiered on September 22, 2011; the first episode attracted 14.1 million viewers and the second episode attracted 14.7 million viewers. The following table shows the number of viewers in themillions for the first 21 episodes of the 2011-2012 season (The Big Bang Theory website, April 17, 2012).
Air Date Viewers(Millions) Air Date Viewers(Millions)
September 22, 2011 14.1 January 12, 2012 16.1
September 22, 2011 14.7 January 19, 2012 15.8
September 29, 2011 14.6 January 26, 2012 16.1
October 6, 2011 13.6 February 2, 2012 16.5
October 13, 2011 13.6 February 9, 2012 16.2
October 20, 2011 14.9 February 16, 2012 15.7
October 27, 2011 14.5 February 23, 2012 16.2
November 3, 2011 16.0 March 8, 2012 15.0
November 10, 2011 15.9 March 29, 2012 14.0
November 17, 2011 15.1 April 5, 2012 13.3
December 8, 2011 14.0
a. Compute the minimum and maximum number of viewers.
b. Compute the mean, medium, and mode.
c. Compute the first and third quartiles.
d. Has viewership grown or declined over the 2011-2012 season? Discuss.
Explanation / Answer
following information has been generated using ms-excel
(a)minimum viewers=13.3 and maximum viewers=16.5
(b) mean=sum/n=15.04=315.9/21=15.04
medain is the middle value of the distribution, after arranging the data in ascendening order or descending order the middle ((n+1)/2=21+1)/2=11th observation is 15. so median=15
the most frequently appearing value in a set of numbers or data points, here 13.6,16.1 and 16.2 appeared most of the times (two times each). so this is the case of multi-model.
(c) the ( n/4)th=(21+1)/4=5.5 =(6 next whole number) 6th observation ( ascendening order) is first quartile quartile i.e.14.1
the ( 3n/4)th=(21+1)/4=16.5 =(17 next whole number) 17th observation ( ascendening order) is first quartile quartile i.e.16.1
(d) viwership is declined as it is 13.3 from the 14.1
n= 21 sum= 315.9 mean=sum/n= 15.0428571 median= 15 mode= 13.6 first quartile= 14.1 third quartile= 16.1Related Questions
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