Descriptive stats
- Mean (Average): The sum of all values divided by the number of values. It gives a measure of central tendency.
- Example: If a study of 50 surgery patients’ recovery times yields times of 5, 6, and 7 days, the mean would be (5+6+7)/3 = 6 days.
- Median: The middle value when data is ordered. This is often used when there are outliers, as the median is less affected by extreme values than the mean.
- Example: For the times [3, 4, 5, 6, 100], the median is 5, whereas the mean would be skewed by 100.
- Mode: The most frequent value in a dataset. For example, in surgical recovery times, if 10 patients had 5 days of recovery time, the mode would be 5 days.
- Range: The difference between the highest and lowest values. It shows the spread of the data.
- Example: If the recovery times of patients range from 2 to 10 days, the range is 10 - 2 = 8 days.
- Variance and Standard Deviation: Measures of how spread out the values in a data set are. Standard deviation is the square root of the variance and is often preferred because it is in the same units as the data.
- High variance or standard deviation indicates a large spread (e.g., patients with a wide range of recovery times).
- Low variance suggests that the recovery times are similar for most patients.
Bringing it into context of surgical research
Study Purpose: A study examining the average recovery time after laparoscopic gallbladder surgery (cholecystectomy).
- Descriptive Statistics Used:
- Mean: The average recovery time for 200 patients was 4.5 days.
- Median: The middle recovery time was 4 days (this might be different from the mean if there are outliers, such as one patient who takes 2 weeks to recover).
- Standard Deviation: The standard deviation of 2 days tells us that most patients recover within 2 days of the average (i.e., between 2.5 to 6.5 days).
- Range: The shortest recovery time was 2 days, and the longest was 14 days.
- Mode: Most patients (about 30%) recover in 4 days, which is the mode.