Question 1
Ten high school students recorded how many hours they slept on a school night: 3, 6.5, 7, 7, 7.5, 7.5, 8, 8, 8.5 and 9. Which statement best describes this distribution?
Psychology statistics calculator: mean, median, SD and percentile
Enter a set of scores to get the mean, median, mode, range and standard deviation, whether the data are skewed, and where any one score sits: its percentile rank and its place on a normal curve.
10 scores
Mean 18.8 · SD 4.75
| Mean | 18.8 |
|---|---|
| Median | 18.5 |
| Mode | 15 |
| Range | 30 − 12 = 18 |
| Standard deviation | 4.75 (sample: 5.01) |
The mean and median are close, so the scores are roughly symmetrical.
A score of 21 has a percentile rank of 70 in this data. On a normal curve with this mean and standard deviation it has a z-score of 0.46, within 1 standard deviation of the mean, where about 68% of scores fall, with about 67.84% of scores below it.
| Mean | The sum of the scores divided by how many there are |
|---|---|
| Range | The highest score minus the lowest |
| Normal curve | About 68% within 1 SD, 95% within 2, 99.7% within 3 |
| Skew | A tail pulls the mean toward it, away from the median |
What the course asks you to calculate
- Mean, median, mode and range from a set of data.
- Interpreting the standard deviation and percentile rank of a score.
- Reading a normal curve: the share of scores within 1, 2 and 3 standard deviations, skew and bimodal distributions.
- Interpreting a correlation coefficient, effect size and statistical significance.
Reading skew quickly
In a positively skewed distribution a few high scores pull the mean above the median; in a negatively skewed one a few low scores pull it below. When data are skewed, the median describes a typical score better than the mean.
Try 2 questions
Question 2
Scores on a sensation-seeking scale are normally distributed with a mean of 50 and a standard deviation of 10. Ari scores 70. About what percent of people taking the scale score below Ari?
Next step
College Board's AP Psychology course page, with the unit and practice weights
Questions people ask
What percentage of scores fall within one standard deviation?
About 68% in a normal distribution; about 95% fall within two and about 99.7% within three.
What is a percentile rank?
The percentage of scores in a group that fall below a given score. A percentile rank of 80 means the score is higher than 80% of the group.
When is the median better than the mean?
When the data are skewed or have outliers: the mean is pulled toward the tail, while the median stays at the middle score.