Respuesta :
Answer:
Option A - 2.2
Step-by-step explanation:
Given : Data of 10 students
The students responses were: 1, 2, 2, 4, 5, 6, 6, 8, 8, 8
To find : The absolute deviation
Solution :
Step 1: We calculate the mean.
[tex]Mean = \frac{\text{Sum of the numbers}}{\text{Total numbers}}[/tex]
[tex]Mean = \frac{1+2+ 2+ 4+ 5+ 6+ 6+ 8+ 8+ 8}{10}[/tex]
[tex]Mean = \frac{50}{10}[/tex]
[tex]Mean = 5[/tex]
Step 2: Then we calculate how far away each data point is from the mean using positive distances these are known as absolute deviations.
Data point Distance from mean
1 |5-1| =4
2 |5-2| =3
2 |5-2| =3
4 |5-4| =1
5 |5-5| =0
6 |5-6| =1
6 |5-6| =1
8 |5-8| =3
8 |5-8| =3
8 |5-8| =3
Step 3: Add the deviations together.
[tex]\Rightarrow 4+3+3+1+0+1+1+3+3+3= 22[/tex]
Step 4: Finally Divide the sum by the number of data points to get mean of absolute deviation.
[tex]\Rightarrow\frac{22}{10}=2.2[/tex]
Therefore,Option A is correct the mean absolute deviation is 2.2.
