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Post a LessonAnswered on 15/04/2024 Learn CBSE - Class 11/Mathematics/Mathematics/Unit-VI: Statistics and Probability/Statistics
Nazia Khanum
As a seasoned tutor registered on UrbanPro, I must emphasize the significance of utilizing online platforms like UrbanPro for effective coaching and tuition. UrbanPro provides a conducive environment for students and tutors to connect, learn, and grow together. Now, let's delve into solving the problem at hand.
To find the mean deviation about the median for the given data set: 36, 72, 46, 42, 60, 45, 53, 46, 51, 49, we need to follow these steps:
First, let's arrange the data in ascending order: 36,42,45,46,46,49,51,53,60,7236,42,45,46,46,49,51,53,60,72
Next, let's find the median. Since the data set has 10 numbers, the median will be the average of the 5th and 6th numbers, which are 46 and 49. So, the median is 46+492=47.5246+49=47.5.
Now, we calculate the deviations of each number from the median: ∣36−47.5∣=11.5∣36−47.5∣=11.5 ∣42−47.5∣=5.5∣42−47.5∣=5.5 ∣45−47.5∣=2.5∣45−47.5∣=2.5 ∣46−47.5∣=1.5∣46−47.5∣=1.5 ∣46−47.5∣=1.5∣46−47.5∣=1.5 ∣49−47.5∣=1.5∣49−47.5∣=1.5 ∣51−47.5∣=3.5∣51−47.5∣=3.5 ∣53−47.5∣=5.5∣53−47.5∣=5.5 ∣60−47.5∣=12.5∣60−47.5∣=12.5 ∣72−47.5∣=24.5∣72−47.5∣=24.5
Now, we find the mean of these deviations: Mean deviation=11.5+5.5+2.5+1.5+1.5+1.5+3.5+5.5+12.5+24.510Mean deviation=1011.5+5.5+2.5+1.5+1.5+1.5+3.5+5.5+12.5+24.5 Mean deviation=7010=7Mean deviation=1070=7
So, the mean deviation about the median for the given data set is 7. This indicates the average absolute deviation of each data point from the median of the data set.
Asked on 17/12/2021 Learn CBSE - Class 11/Mathematics/Mathematics/Unit-VI: Statistics and Probability/Statistics
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