Evidence Based Medicine
Statistics
What is the median of the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13
Answer:
The median is the middle value of a data set that has been placed in numerical order starting with the smallest value and ending with the largest value. With an even number of data values, the median is the average of the two values that lie on either side of the midline. It is the point which has half of the observations above it and half of the observations below it. The numbers in order = 13, 13, 13, 13, 14, 14, 16, 18, 21 and sample size (n) = 9. The median = [(n+1)/2]th value = 5th value = 14Measures of Central Tendency
Evidence Based Medicine / Statistics
Last Updated: 22nd November 2022
There are three measures of central tendency: mean, median and mode.
- Normal distribution (no skew): Mean = median = mode
- Positive skew (skewed to the right): Mean > median > mode
- Negative skew (skewed to the left): Mean < median < mode
Mean
The mean is the arithmetic average, calculated by summing all of the values of a data set and dividing this sum by the number of observations in the data set.
The mean is used in normally distributed data as it uses all of the data set and roughly reflects the sampling distribution. However the mean is distorted by outliers and skewed data, where the median should be used instead.
Median
The median is the middle value of a data set that has been placed in numerical order starting with the smallest value and ending with the largest value. With an even number of data values, the median is the average of the two values that lie on either side of the midline. It is the point which has half of the observations above it and half of the observations below it.
The median is similar to the mean if the data is symmetrical, less than the mean if the data are skewed to the right and greater than the mean if the data are skewed to the left.
The median is not distorted by outliers or skewed data but ignores most of the data values and so it can be shown to be less efficient than the mean.
Mode
The mode is the value that is observed most frequently in a data set.
The mode is rarely used as a summary measure. It is easily determined for categorical data but ignores most of the information and does not reflect sampling distribution.
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- Biochemistry
- Blood Gases
- Haematology
| Biochemistry | Normal Value |
|---|---|
| Sodium | 135 – 145 mmol/l |
| Potassium | 3.0 – 4.5 mmol/l |
| Urea | 2.5 – 7.5 mmol/l |
| Glucose | 3.5 – 5.0 mmol/l |
| Creatinine | 35 – 135 μmol/l |
| Alanine Aminotransferase (ALT) | 5 – 35 U/l |
| Gamma-glutamyl Transferase (GGT) | < 65 U/l |
| Alkaline Phosphatase (ALP) | 30 – 135 U/l |
| Aspartate Aminotransferase (AST) | < 40 U/l |
| Total Protein | 60 – 80 g/l |
| Albumin | 35 – 50 g/l |
| Globulin | 2.4 – 3.5 g/dl |
| Amylase | < 70 U/l |
| Total Bilirubin | 3 – 17 μmol/l |
| Calcium | 2.1 – 2.5 mmol/l |
| Chloride | 95 – 105 mmol/l |
| Phosphate | 0.8 – 1.4 mmol/l |
| Haematology | Normal Value |
|---|---|
| Haemoglobin | 11.5 – 16.6 g/dl |
| White Blood Cells | 4.0 – 11.0 x 109/l |
| Platelets | 150 – 450 x 109/l |
| MCV | 80 – 96 fl |
| MCHC | 32 – 36 g/dl |
| Neutrophils | 2.0 – 7.5 x 109/l |
| Lymphocytes | 1.5 – 4.0 x 109/l |
| Monocytes | 0.3 – 1.0 x 109/l |
| Eosinophils | 0.1 – 0.5 x 109/l |
| Basophils | < 0.2 x 109/l |
| Reticulocytes | < 2% |
| Haematocrit | 0.35 – 0.49 |
| Red Cell Distribution Width | 11 – 15% |
| Blood Gases | Normal Value |
|---|---|
| pH | 7.35 – 7.45 |
| pO2 | 11 – 14 kPa |
| pCO2 | 4.5 – 6.0 kPa |
| Base Excess | -2 – +2 mmol/l |
| Bicarbonate | 24 – 30 mmol/l |
| Lactate | < 2 mmol/l |
