Question

Following are the global sales of the top 40 rap concerts of the 1990’s. Please make a Stem and Leaf Plot of the data. Then, evaluate the data and without making any explicit calculations, determine which is greater – the median of the distribution or the mean?

Rap Concerts in Millions:

2797	2789	2187	2068	2048	1670	1656	1518	1515	1402
1346	1341	1332	1308	1274	1263	1242	1236	1214	1159
1153	1148	1131	1128	1123	1120	1108	1104	1081	1073
1066	1066	1056	1055	1050	1045	1034	1030	1028	1027

Answer 1

The Stem - Leaf plot is given below -

Stem	Leaf
102	7, 8
103	0, 4
104	5
105	0, 5, 6
106	6, 6
107	3
108	1
110	4, 8
112	0, 3, 8
113	1
114	8
115	3, 9
121	4
123	6
124	2
126	3
127	4
130	8
133	2
134	1, 6
140	2
151	5, 8
165	6
167	0
204	8
206	8
218	7
278	9
279	7

Looking at the plot one can say that,

The Mean of the distribution > The Median of the distribution

because in the first 15 - 20 data values there is relatively smaller dispersion, that is, the data values were all lying in a relatively small range, but in the next half there is a larger dispersion of the values, this set of data values were all lying in a pretty large rage, at least a range bigger than the earlier one.

Since, Median depends more on the position of the data point more than the value of the data point, hence it would be smaller than the mean, which depends on the value of the data point