Answer:
B -0.104
Step-by-step explanation:
Step 1: Write the formula for correlation
r = total xy
√Total x² x Total y²
Step 2: Make a table to calculate all values
Table is attached in the picture below
Step 3 : Solve
Mean of X = Total X/ Total number of X
= 507/12
= 106.33
Mean of Y = Total Y/ Total number of Y
= 1276/ 12
= 42.25
r = total xy
√Total x² x Total y²
r = -352.05/ √3656.25 x 3122.66698
r = -0.104
-0.104 is negative
This negative correlation means there is an inverse correlation between variables.
Answer:
B. According to this data, there is a negative correlation between age and IQ.
Step-by-step explanation:
Correlation shows the strength of relation between two variables. The formula used to calculate correlation is:
[tex]Correlation(r) = \frac{Cov(x, y)}{\sigma_{x}\sigma_{y}}= \frac{E(x-\mu_{x})(y-\mu_{y})}{\sigma_{x}\sigma_{y}}[/tex]
where, Cov(x,y) = Covariance of x and y
[tex]\sigma_{x} [/tex] = standard deviation of x
[tex]\sigma_{y} [/tex] = standard deviation of y
[tex]\mu_{x} [/tex] = mean of x
[tex]\mu_{y} [/tex] = mean of y
and, E denotes the Expectation.
The value of the correlation lies between -1 to +1.
If the value of correlation lies between -1 to 0 then it is known as a negative correlation.
and, If the value of correlation lies between 0 to 1 then it is known as a positive correlation.
Using the above formula of correlation we get Correlation (r) = -0.1225.
Thus, there is negative correlation between age and IQ.
We can also use a correlation calculator for getting the value of correlation.
Hence, option (B) is correct.
