Question

What is the standard deviation of the following data set rounded to the nearest tenth

Answer 1

Given data set is {1, 1.12, 4, 1.28, 4.1, 5.3}

Step 1: Finding Mean.

Mean = (1 + 1.12 + 4 + 1.28 + 4.1 + 5.3)/6 = 16.8/6 = 2.8

Step 2: Finding square of difference between mean and data points.

(1 - 2.8)², (1.12 - 2.8)², (4 - 2.8)², (1.28 - 2.8)², (4.1 - 2.8)², (5.3 - 2.8)²

3.24, 2.8224, 1.44, 2.3104, 1.69, 6.25

Step 3: Finding Mean of above numbers (also called variance).

Variance = (3.24 + 2.8224 + 1.44 + 2.3104 + 1.69 + 6.25)/6 = 17.7528/6 = 2.9588

Step 4: Finding square-root of variance (also called standard deviation).

Standard Deviation =  $\sqrt{2.9588} = 1.720116275 \approx 1.7$

Hence, option D is correct, i.e. Standard Deviation = 1.7

Answer 2

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.