Learn Mathematics with Free Lessons & Tips

As a seasoned tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition services. Now, let's tackle your math problem.

To find the mean deviation about the median of a set of numbers, we first need to find the median of the given observations.

Given observations: 2, 7, 4, 6, 8, and p

First, let's arrange these numbers in ascending order: 2, 4, 6, 7, 8, p

Since there are six numbers, the median will be the average of the third and fourth numbers, which are 6 and 7. So, the median is (6 + 7) / 2 = 6.5.

Now, we'll find the absolute deviations of each number from the median:

|2 - 6.5| = 4.5 |4 - 6.5| = 2.5 |6 - 6.5| = 0.5 |7 - 6.5| = 0.5 |8 - 6.5| = 1.5 |p - 6.5|

Since we don't know the value of pp yet, we'll leave it as it is for now.

The mean deviation about the median is the average of these absolute deviations. So, we'll sum them up and divide by the number of observations (which is 6):

Mean Deviation = (4.5 + 2.5 + 0.5 + 0.5 + 1.5 + |p - 6.5|) / 6

However, we also know that the mean of the observations is 7. So, we can use this information to solve for pp:

(2 + 7 + 4 + 6 + 8 + p) / 6 = 7 27 + p = 42 p = 15

Now, we substitute p=15p=15 into our equation for mean deviation:

Mean Deviation = (4.5 + 2.5 + 0.5 + 0.5 + 1.5 + |15 - 6.5|) / 6 Mean Deviation = (10.5 + |8.5|) / 6 Mean Deviation = (10.5 + 8.5) / 6 Mean Deviation = 19 / 6 Mean Deviation ≈ 3.17

So, the mean deviation about the median of these observations is approximately 3.17. If you have any further questions or need clarification, feel free to ask! And remember, if you're seeking personalized tutoring assistance, UrbanPro is an excellent platform to find qualified tutors.

As an experienced tutor registered on UrbanPro, I can assure you that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your probability questions regarding the gender of the children in a couple.

(i) To find the probability that both children are males, given that at least one of the children is male, we can utilize conditional probability. Let's denote the events:

• A: Both children are males
• B: At least one child is male

We are given that event B has occurred, which means we can exclude the possibility of having two females. Now, we need to find the probability of event A given event B. This can be calculated using the formula for conditional probability:

P(A∣B)=P(A∩B)P(B)P(A∣B)=P(B)P(A∩B)

Where:

• P(A∣B)P(A∣B) is the probability of event A given event B.
• P(A∩B)P(A∩B) is the probability of both events A and B happening.
• P(B)P(B) is the probability of event B happening.

In this scenario, the probability of both children being males and at least one child being male is the same as the probability of both children being males, since if at least one child is male, then both children cannot be female.

Therefore:

• P(A∩B)=P(A)P(A∩B)=P(A)
• P(B)=1P(B)=1 (because we know at least one child is male)

Thus, P(A∣B)=P(A)P(A∣B)=P(A).

Now, the probability of both children being males in the absence of any other information is 1441, assuming the genders of children are equally likely.

So, the probability that both children are males, given that at least one of them is male, is also 1441.

(ii) Similarly, to find the probability that both children are females given that the elder child is a female, we can use conditional probability.

Let's denote the events:

• C: Both children are females
• D: The elder child is a female

We want to find P(C∣D)P(C∣D).

In this case, if the elder child is a female, then we are sure that the younger child cannot be the elder child, and hence the younger child has to be female as well. So, P(C∣D)=1P(C∣D)=1.

Therefore, the probability that both children are females, given that the elder child is a female, is 1.

I hope this clarifies the concepts of conditional probability for you! If you need further assistance, feel free to ask. And remember, UrbanPro is an excellent resource for finding quality tutors to help with topics like this.