Question

In: Statistics and Probability

All Time Box Office Revenues Aggregated by Months Rank Month Gross Movies Tracked 1 February, 2009...

All Time Box Office Revenues Aggregated by Months

Rank

Month

Gross

Movies Tracked

1

February, 2009

796,343,640

161

2

February, 2010

745,693,066

173

3

February, 2008

659,270,466

193

4

February, 2004

666,141,251

201

5

February, 2007

693,647,238

176

6

February, 2003

613,460,961

207

7

February, 2005

692,957,988

185

8

February, 2006

652,426,175

193

9

February 2002

529,353,345

98
  1. Calculate the mean for the gross revenues.
  2. Calculate the mean for the Movies tracked.
  3. Calculate the standard deviation for the movies tracked.

Solutions

Expert Solution

1. Mean for the gross revenues.

The sample size is n=9. The provided sample data along with the data required to compute the sample mean is shown in the table below:

Gross Revenue Gross Revenue2
796343640 634163192968449600
745693066 556058148680480356
659270466 434637547339857156
666141251 443744166283845001
693647238 481146490785028644
613460961 376334350671043521
692957988 480190773133008144
652426175 425659913825130625
529353345 280214963862689025
Sum = 6049294130 4.1121495475495E+18

The sample mean is computed as follows:

2. Mean for the Movies tracked.

The sample size is n=9. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

Movies Tracked Movies Tracked2
161 25921
173 29929
193 37249
201 40401
176 30976
207 42849
185 34225
193 37249
98 9604
Sum = 1587 288403

The sample mean is computed as follows:

3. The standard deviation for the movies tracked.

Also, the sample variance is

Therefore, the sample standard deviation s is

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!

orchestra answered 1 year ago
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