1, 1.12, 4, 1.28, 4.1, 5.3
To find standard deviation, first we have to find the mean of the data set.
To find mean we have to add them and divide it by the number of terms given. Here 6 numbers given.
Mean = (1+ 1.12 + 4 + 1.28 + 4.1 + 5.3)/6 = 16.8 / 6 = 2.8
Now we have to subtract the mean from each number and have to find square of it.
(1- 2.8)² = (-1.8)² = 3.24
(1.12-2.8)² = (-1.68)² = 2.8224
(4-2.8)² = (1.2)² = 1.44
(1.28 -2.8)² = (-1.52)² = 2.3104
(4.1 - 2.8)² = (1.3)² = 1.69
(5.3 - 2.8)² = (2.5)² = 6.25
Now we have to add them all.
3.24 + 2.8224 + 1.44+ 2.3104 + 1.69 + 6.25 = 17.7528
Now to get standard deviation we have to divide it by total number of terms which is 6 here and then have to find square root of it.
So, standard deviation =√[ (17.7528) / 6] =√(2.9588) = 1.720116
So the required answer is, standard deviation = 1.7 ( approximately to the nearest tenth)
The correct option is D.
