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98
82

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Evidence Based Medicine

Statistics

Question 135 of 180

What is the interquartile range of the following data set: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70

Answer:

5, 10, 15 /20, 25, 30 /35, 40, 45 /50, 60, 70 Sample size (n) = 12 Median = [(n+1)/2]th value = (12+1)/2 = 6.5 = halfway between 6th and 7th value = (30 +35)/2 = 32.5 The lower (first) quartile = halfway between 15 and 20 = 17.5 The upper (third) quartile = halfway between 45 and 50 = 47.5 The interquartile range is the difference between the upper quartile and lower quartile = 47.5 - 17.5 = 30

Interquartile Range

It is useful to have some measure of the variation of observations about the mean or median. Measures of variation differ whether the data is normally distributed or non-normally distributed:

  • In a normally distributed data set, the mean and standard deviation are used to describe variation.
  • In a non-normally distributed data set, the median and interquartile range are used to describe variation.

Range

The range states the difference between the largest and smallest values in the data set and can be given as two numbers or a single value.

The range however does not give much indication of the average spread of observations about the mean and provides a misleading measure of spread if there are outliers.

Interquartile Range

A more robust approach is to determine the interquartile range, which is largely unaffected by sample size, and usually unaffected by outliers.

The interquartile range (IQ) is a measure of spread given by the difference between the first quartile (the value below which 25% of the observations lie) and the third quartile (the value below which 75% of the observations lie). It focuses on the spread of the middle 50% of the values in an ordered data set.

Box and Whisker Plot

A boxplot is a vertical or horizontal rectangle used to display the interquartile range, with the ends of the rectangle corresponding to the upper and lower quartiles of the data values. The box contains 50% of the data values. A line drawn through the rectangle corresponds to the median value. Whiskers, starting at the ends of the rectangle usually indicate the minimum and maximum values, therefore the entire box and whisker plot represents the range. Any outliers can be plotted independent of the box and whisker plot.

Modified by FRCEM Success. Original by Madyno (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0 , via Wikimedia Commons

Box and Whisker Plot. (Image modified by FRCEM Success. Original by Madyno (Own work) [CC BY-SA 3.0 , via Wikimedia Commons)

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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

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