what is the mean deviation of the data:8,9,12,15,16,20,24,30,32,34?
Answers
Answer:
8
Step-by-step explanation:
mean=8+9+12+15+16+20+24+30+32+34/10=20
mean deviation=20-8=12
20-9=11........20-34=14
mean deviation=12+11+8+5+4+0+10+12+14/10=8
Ans:8
Given :- what is the mean deviation of the data:8,9,12,15,16,20,24,30,32,34 ?
Solution :-
As we know that,
- Mean is equal to average of numbers.
- Mean = (sum of all observations.) / (Total number of observations.)
So,
→ sum of all observations = 8 + 9 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 34 = 200
and,
→ Total number of observations are = 10 .
Therefore,
→ Mean = (sum of all observations.) / (Total number of observations.)
→ Mean = (200 / 10)
→ Mean = 20
Now, we need to find the distance of all the given values from mean . { ignore minus sign .}
So,
- 20 - 8 = 12
- 20 - 9 = 11
- 20 - 12 = 8
- 20 - 15 = 5
- 20 - 16 = 4
- 20 - 20 = 0
- 24 - 20 = 4
- 30 - 20 = 10
- 32 - 20 = 12
- 34 - 20 = 14
Now, we know that,
- Mean deviation = (sum of the distance of each value from mean) / (Total number of observations.)
Therefore,
→ sum of distance of each value from mean = 12 + 11 + 8 + 5 + 4 + 0 + 4 + 10 + 12 + 14 = 80
Hence,
→ Mean deviation = 80 / 10 = 8 (Ans.)
Hence, mean deviation of given data is 8.
Learn more :-
The mean and standard deviation of a data which is comprised of a set of ten positive numbers are 8 and 2 respectively ....
https://brainly.in/question/26639131