Standard deviation (tabular method) in real world problems worksheets, solved worksheet problems or exercises with step-by-step work, formative assessment as online test, calculator and more learning resources to learn, practice, assess and master the basic math skills of statistics.
xi | (𝑥i − x̄) | (𝑥i − x̄)2 |
---|---|---|
8 | 2.5 | 6.25 |
5 | -0.5 | 0.25 |
2 | -3.5 | 12.25 |
4 | -1.5 | 2.25 |
10 | 4.5 | 20.25 |
1 | -4.5 | 20.25 |
7 | 1.5 | 2.25 |
3 | -2.5 | 6.25 |
6 | 0.5 | 0.25 |
9 | 3.5 | 12.25 |
∑𝑥i = 55 | ∑(𝑥i − x̄)2 = 82.5 | |
x̄ = 55/10 = 5.5 |
xi | (𝑥i − μ) | (𝑥i − μ)2 |
---|---|---|
6 | -9 | 81 |
8 | -7 | 49 |
10 | -5 | 25 |
12 | -3 | 9 |
14 | -1 | 1 |
16 | 1 | 1 |
18 | 3 | 9 |
20 | 5 | 25 |
22 | 7 | 49 |
24 | 9 | 81 |
∑𝑥i = 150 | ∑(𝑥i − μ)2 = 330 | |
x̄ = 150/10 = 15 |
xi | (𝑥i − μ) | (𝑥i − μ)2 |
---|---|---|
32 | -2.38 | 5.664 |
35 | 0.62 | 0.384 |
37 | 2.62 | 6.864 |
30 | -4.38 | 19.184 |
33 | -1.38 | 1.904 |
36 | 1.62 | 2.624 |
35 | 0.62 | 0.384 |
37 | 2.62 | 6.864 |
∑𝑥i = 275 | ∑(𝑥i − μ)2 = 43.878 | |
x̄ = 275/8 = 34.38 |
xi | (𝑥i − μ) | (𝑥i − μ)2 |
---|---|---|
310 | 10 | 100 |
290 | -10 | 100 |
320 | 20 | 400 |
280 | -20 | 400 |
300 | 0 | 0 |
290 | -10 | 100 |
320 | 20 | 400 |
310 | 10 | 100 |
280 | -20 | 400 |
∑𝑥i = 2700 | ∑(𝑥i − μ)2 = 2000 | |
x̄ = 2700/9 = 300 |
xi | (𝑥i − μ) | (𝑥i − μ)2 |
---|---|---|
1 | -4.5 | 20.25 |
2 | -3.5 | 12.25 |
3 | -2.5 | 6.25 |
4 | -1.5 | 2.25 |
5 | -0.5 | 0.25 |
6 | 0.5 | 0.25 |
7 | 1.5 | 2.25 |
8 | 2.5 | 6.25 |
9 | 3.5 | 12.25 |
10 | 4.5 | 20.25 |
∑𝑥i = 55 | ∑(𝑥i − μ)2 = 82.5 | |
x̄ = 55/10 = 5.5 |
xi | (𝑥i − μ) | (𝑥i − μ)2 |
---|---|---|
17.8 | 2.8 | 7.84 |
19.2 | 4.2 | 17.64 |
16.3 | 1.3 | 1.69 |
12.5 | -2.5 | 6.25 |
12.8 | -2.2 | 4.84 |
11.4 | -3.6 | 12.96 |
∑𝑥i = 90 | ∑(𝑥i − μ)2 = 51.22 | |
x̄ = 90/6 = 15 |
xi | (𝑥i − x̄) | (𝑥i − x̄)2 |
---|---|---|
18 | -1.2 | 1.44 |
22 | 2.8 | 7.84 |
19 | -0.2 | 0.04 |
25 | 5.8 | 33.64 |
12 | -7.2 | 51.84 |
∑𝑥i = 96 | ∑(𝑥i − x̄)2 = 94.8 | |
x̄ = 96/5 = 19.2 |
xi | (𝑥i − x̄) | (𝑥i − x̄)2 |
---|---|---|
112 | -3.75 | 14.063 |
100 | -15.75 | 248.063 |
127 | 11.25 | 126.563 |
120 | 4.25 | 18.063 |
134 | 18.25 | 333.063 |
118 | 2.25 | 5.063 |
105 | -10.75 | 115.563 |
110 | -5.75 | 33.063 |
∑𝑥i = 926 | ∑(𝑥i − x̄)2 = 893.504 | |
x̄ = 926/8 = 115.75 |
xi | (𝑥i − x̄) | (𝑥i − x̄)2 |
---|---|---|
7.7 | 0.125 | 0.016 |
7.4 | -0.175 | 0.031 |
7.3 | -0.275 | 0.076 |
7.9 | 0.325 | 0.106 |
∑𝑥i = 30.3 | ∑(𝑥i − x̄)2 = 0.229 | |
x̄ = 30.3/4 = 7.575 |
xi | (𝑥i − x̄) | (𝑥i − x̄)2 |
---|---|---|
2 | -1.5 | 2.25 |
6 | 2.5 | 6.25 |
5 | 1.5 | 2.25 |
3 | -0.5 | 0.25 |
2 | -1.5 | 2.25 |
3 | -0.5 | 0.25 |
∑𝑥i = 21 | ∑(𝑥i − x̄)2 = 13.5 | |
x̄ = 21/6 = 3.5 |