| Tag | Value |
|---|---|
| file | Descriptive-statistics_eur-descriptive-126-en_eur-descriptive-126-en |
| name | eur-descriptive-126-en |
| section | Descriptive statistics/Summary Statistics/Measures of Spread/Standard Deviation |
| type | num |
| solution | 1.304 |
| tolerance | 0.01 |
| Type | Calculation |
| Program | Calculator |
| Language | English |
| Level | Statistical Literacy |
Below you find the scores of six students on the course 1.1 exam (social psychology) and the course 1.3 exam (statistics). For both exam scores calculate the standard deviation.
| Students | Exam Course 1.1 | Exam Course 1.3 |
|---|---|---|
| 1 | 7.5 | 6.8 |
| 2 | 6.2 | 5.4 |
| 3 | 5.2 | 7.6 |
| 4 | 8.2 | 7.6 |
| 5 | 9.2 | 8.4 |
| 6 | 6.9 | 4.7 |
Calculate standard deviation of the exam scores for course 1.3
| Students | Exam Course 1.3 | Squared Deviation 1.3 | |
|---|---|---|---|
| 1 | 6.8 | (6.8 ‐ 6.75)(6.8 ‐ 6.75) | |
| 2 | 5.4 | (5.4 ‐ 6.75)(5.4 ‐ 6.75) | |
| 3 | 7.6 | (7.6 ‐ 6.75)(7.6 ‐ 6.75) | |
| 4 | 7.6 | (7.6 ‐ 6.75)(7.6 ‐ 6.75) | |
| 5 | 8.4 | (8.4 ‐ 6.75)(8.4 ‐ 6.75) | |
| 6 | 4.7 | (4.7 ‐ 6.75)(4.7 ‐ 6.75) | |
| Sum | 40.5 | 10.195 | |
| Mean | 6.75 | 1.699 |
The mean is calculated by summing the scores on the exam and dividing this sum by the number of participants:
Mean Exam 1.3 =
A deviation score is calculated by subtracting the individual score from the mean. The variance is calculated by squaring these deviation scores, summing those and divide this sum by N.
Variance Exam 1.3 =
The standard deviation is calculated by taking the square root of the variance.
Standard deviation Exam 1.1 =