The mean of 2, 7, 4, 6, 8 and p is 7. Find the mean deviation about the median of these observations.

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. read less