Chapter 1.3, Problem 87E

(a)

To determine

To estimate: the mean and median of the distribution.

Answer to Problem 87E

Median is 6 and mean is 7.01

Explanation of Solution

Given:

  

Calculation:

From the given histogram of domain name length (in number of letters in the name, not including the extension.com and .org) for 500 most popular websites We have calculated mean as follows:

Domain name length (X)	Frequency (f)	fX
2	10	20
3	40	120
4	42	168
5	58	290
6	105	630
7	60	420
8	58	464
9	38	342
10	27	270
11	18	198
12	20	240
13	10	130
14	5	70
15	5	75
16	1	16
17	3	51

We find the Mean

  $\begin{array}{l}\overline{X}=\frac{{\displaystyle \sum fX}}{{\displaystyle \sum f}}\\ =\frac{3504}{500}\\ \overline{X}=7.01\end{array}$

Median is calculated as follows:

Domain name length(X)	Frequency (f)	Cumulative frequency (cf)
2	10	10
3	40	50
4	42	92
5	58	150
6	105	255
7	60	315
8	59	374
9	38	412
10	30	442
11	28	470
12	20	490
13	10	500
14	5	505
15	5	510
16	2	512
17	4	516

  $\begin{array}{l}M=\frac{N+1}{2}\\ N=\text{Cumilative}\text{frequency}\\ =\frac{500+1}{2}\\ M=250.5\end{array}$

The median is 6

Conclusion:

Therefore, median is 6 and mean is 7.01

(b)

To determine

To find: which measure of center is chosen

Answer to Problem 87E

Here, median is chosen

Explanation of Solution

To justify that shorter domain names were more popular than median is chosen because data is skewed towards right in that case means is greater than median and median is towards shorter length.