Calculate p ̅.

x1 20
n1 50
x2 55
n2 100

To calculate the average proportion p̅, you need to first calculate the proportions for each sample and then take their average.

The proportion, denoted as p, is calculated by dividing the number of successes (x) by the sample size (n). In this case, you have two sets of data:

Sample 1:
x1 = 20 (number of successes)
n1 = 50 (sample size)

Sample 2:
x2 = 55 (number of successes)
n2 = 100 (sample size)

To calculate the proportion for sample 1, divide x1 by n1:
p₁ = x₁ / n₁ = 20 / 50 = 0.4

To calculate the proportion for sample 2, divide x2 by n2:
p₂ = x₂ / n₂ = 55 / 100 = 0.55

Now that you have the proportions for each sample, you can calculate the average proportion p̅ by adding the individual proportions and dividing by the number of samples:
p̅ = (p₁ + p₂) / 2 = (0.4 + 0.55) / 2 = 0.95 / 2 = 0.475

Therefore, the average proportion p̅ is 0.475.