Final answer:
To find the value of p that makes the mean of the data 18.75, the sum of the products of the frequencies and the values is divided by the total number of elements, resulting in p being equal to 20.
Step-by-step explanation:
The question pertains to finding the missing value p given that the mean of the data set is 18.75. To solve this, we can use the formula for the mean, which is the sum of the products of the frequencies (fi) and the values (xi) divided by the total number of elements in the data set (n).
The formula for the mean is:
mean = Σ(fi*xi)/n
Plugging in the provided values:
18.75 = [(5*10) + (10*15) + (7*p) + (8*25) + (2*30)]/32
First, we calculate the sum of products for the given values:
(5*10) + (10*15) + (8*25) + (2*30) = 50 + 150 + 200 + 60 = 460
Now, let's include our unknown p:
18.75 = (460 + 7p) / 32
Multiplying both sides by 32 gives:
600 = 460 + 7p
Subtracting 460 from both sides, we get:
140 = 7p
Dividing both sides by 7 gives:
p = 20
Therefore, the value of p that makes the mean of the data 18.75 is 20.