Question

At a recent concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the beginning of the year. The following data were collected:

Age	62	57	40	49	67	54	43	65	54	41
# of Concerts	6	5	4	3	5	5	2	6	3	1
Age	44	48	55	60	59	63	69	40	38	52
# of Concerts	3	2	4	5	4	5	4	2	1	3

Which of the following is true for this data?

	A.	The younger the respondent the more concerts he/she has attended.
	B.	The younger the respondent the less concerts he/she has attended.
	C.	The relationship between age and the number of concerts attended is insignificant.

Answer 1

The answer to this question can be given using the correlation value between the two variables that is age and the no.of concerts attended.

Correlation value gives the relationship between the two variables. If the value of correlation is positive we can conclude that the relationship between the two variables is positive that means as the value of one variable increases the value of other variable also increases. If the value of correlation is negative we can conclude that the relationship between the two variables is negative that means as the value of one variable increases the value of other variable decreases.

The correlation values ranges from -1 to 1 . When the values is near to 1 we say that there is a strong positive correlation and when the value is near to -1 we say that there is strong negative correlation between the two variables.

The correlation value or correlation matrix can be found by using the data analysis option in excel.

So here the value of correlation between the variables age and the no.of concerts attended is 0.8020 which is positive . So we can conclude that as the age increases the no.of concerts attended also increases.

The conclusion can also be drawn using scatter plot.

The scatter plot of the given data looks like -

Her also one can see that as age increases the no.of concerts attended also increases.

Conclusion: As age increases the no.of concerts attended increases.

Answer : The younger the respondent the less concerts he/she has attended.