Question

Identify the central tendency you feel is the most representative of the data and justify your answer. The total mean =54.97    The total median is 55 and the total Mode is 29

California	39	41	49	55	58	59	59	60	69	71	76	77	78	80	81	82	83	88	89	93		69.35	73.5	59
Conneticut	20	20	29	39	40	50	53	56	56	58	59	60	60	62	66	69	70	71	77	81		54.8	58.5	20
Delaware	10	22	30	35	35	40	41	42	42	55	62	63	68	68	68	70	70	77	88	89		53.75	58.5	68
New York	20	29	29	30	33	39	49	51	52	55	55	55	59	65	68	70	78	84	88	88		54.85	55	55
North Carolina	22	27	27	29	29	29	37	40	43	44	46	48	48	48	50	50	52	54	58	61		42.1	45	29

Answer 1

Here clearly we can see that the total mean and total median is same (approx 55) while the mode is 29. We know when mode is less than mean and median , we said the data are positively skewed that is the data is not symmetrical. The tail is towards the right side and cluster of data lies in left side. This goes the scenario of right skewed data which is actually over here.

Now coming to the selection of best suitable measures of central tendency over here. We know mode is used to measure nominal data. While median is used to measure ordinal data and skewed data. And mean is best suited when data are symmetrical.

So we can now say that here median is the best representation of the data as the measure of central tendency. It is because median is less affected by outliers or skewed data that is data present at extremes as compared to mean when the data is not symmetrical. Mean gets affected with addition or subtraction of any value in a dataset but median is not gets so much affected for that. Hence for skewed (like here) data,median is more suitable than mean.

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