Question

For the following data​ (a) display the data in a scatter​ plot, (b) calculate the correlation coefficient​ r, and​ (c) make a conclusion about the type of correlation. The ages​ (in years) of 6 children and the number of words in their vocabulary ​ Age, x 1 2 3 4 5 6

Vocabulary​ size, y 150 1100 1150 1800 2050 2700

A] The correlation coefficient r is

Answer 1

a)

Scatter Plot:

b)

Age (X)	Vocabulary Size (Y)	X2	Y2	X*Y
1	150	1	22500	150
2	1100	4	1210000	2200
3	1150	9	1322500	3450
4	1800	16	3240000	7200
5	2050	25	4202500	10250
6	2700	36	7290000	16200

Therefore the correlation coefficient r is 0.9789.

c)

Since the correlation is positive and close to 1, therefore we can say that age and vocabulary size are highly positively correlated. That is, as age increases then the number of words in their vocabulary also increases.