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Domain names When it comes to Internet domain names, is shorter better? According to one ranking of Web sites in 2008, the top 8sites (by number of

鈥渉its鈥) were yahoo.com, google.com, youtube.com, live.com, msn.com, myspace.com, wikipedia.org, and facebook.com. These familiar sites certainly have short domain names. The histogram below shows the domain name lengths (in a number of letters in the name, not including the extensions .com and .org) for the 500 most popular Web sites.

(a) Estimate the mean and median of the distribution. Explain your method clearly.

(b) If you wanted to argue that shorter domain names were more popular, which measure of the center would you choose鈥攖he mean or the median? Justify your answer.

Short Answer

Expert verified

Part (a) Median is 6 and mean is 7.01

Part (b) Here, median is chosen.

Step by step solution

01

Part (a) Step 1: Given information

Given graph :

02

Part (a) Step 2: Concept

The mean of a data set is determined by adding all of the numbers in the set and dividing by the number of values in the set. The median is the value in the middle of a data set when it is arranged from smallest to largest. The mode is the number that appears the most frequently in a data set.

03

Part (a) Step 3: Calculation

For the 500 most popular websites, a histogram of domain name length (in number of letters in the name, excluding the extensions.com and.org) was created. The following is how we calculated the mean:

Domain name lengthFrequency (f)fx
21020
340120
442168
558290
6105630
760420
858464
938342
1027270
1118198
1220240
1310130
14570
15575
16116
17351

We find the Mean X=fXfX=3504500X=7.04

Median is calculated as follows:

Domain name length (X)Frequency (f)Commutative frequency
21010
34050
44292
558150
6105255
760315
859374
938412
1030442
1128470
1220490
1310500
145505
155510
162512
174516

M=N+12N=Cumilativefrequency=500+12M=250.5

The median is 6

Therefore, the median is 6and mean is 7.01

04

Part (b) Step 1: Explanation

To justify that shorter domain names were more popular than the median, the data was skewed to the right, so the means were bigger than the median, and the median was shorter.

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