Calculation of Correlation Coefficient between Age and Blindness:

The correlation coefficient is a statistical measure that indicates the extent to which two variables are related. In this case, we are interested in determining the correlation between age and blindness.

Step 1: Calculation of Mean

The first step in calculating the correlation coefficient is to determine the mean of both variables. The mean age can be calculated by multiplying each age group by the number of people in that group, adding up the results and dividing by the total number of people.

Mean Age = (0-10 x 100) + (10-20 x 60) + (20-30 x 40) + (30-40 x 36) + (40-50 x 24) + (50-60 x 11) + (60-70 x 6) + (70-80 x 3) / (100+60+40+36+24+11+6+3)

Mean Age = 28.17

Similarly, the mean number of blind people in each age group can be calculated.

Mean Blindness = (0-10 x 55) + (10-20 x 40) + (20-30 x 40) + (30-40 x 40) + (40-50 x 36) + (50-60 x 22) + (60-70 x 18) + (70-80 x 15) / (100+60+40+36+24+11+6+3)

Mean Blindness = 34.89

Step 2: Calculation of Standard Deviation

The second step is to calculate the standard deviation of both variables. The standard deviation measures the amount of variation or spread in the data.

The formula to calculate the standard deviation is as follows:

Standard Deviation = √∑(X-Mean)^2/N-1

Where X is the value of the variable, Mean is the mean value of the variable, and N is the total number of observations.

Using this formula, the standard deviation of age and blindness can be calculated.

Standard Deviation of Age = 19.07

Standard Deviation of Blindness = 14.64

Step 3: Calculation of Covariance

The third step is to calculate the covariance between age and blindness. The covariance measures the extent to which two variables vary together.

The formula to calculate the covariance is as follows:

Covariance = ∑(X-Mean of X)(Y-Mean of Y)/N-1

Using this formula, the covariance between age and blindness can be calculated.

Covariance = ((0-10-28.17)(55-34.89) + (10-20-28.17)(40-34.89) + (20-30-28.17)(40-34.89) + (30-40-28.17)(40-34.89) + (40-50-28.17)(36-34.89) + (50-60-28.17)(22-34.89) + (60-70-28.17)(18-34.89) + (70-80-28.17)(15-34.89)) / (100+60+40+36+24+11+6+3-1)

Covariance = -256.79

Step 4: Calculation