Updated: 8/5/2018

Statistical Distribution

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Descriptive Statistics
  • Mean
    • Average of all observation
    • Mean = (sum of all observations)/(sample size)
  • Median 
    • The middle value of all observations  
    • If sample size is odd
      • Median = ((n+1)/2)th largest value
    • If the sample size is even
      • Median = the average of the (n/2)th and ((n/2)+1)th largest value 
  • Mode
    • The most commonly occurring value
    • If there is more than one most commonly occurring value, there are as many modes as most commonly occurring values   
Types of Distributions
  • Normal
    • aka Gaussian, bell-shaped
    • Mean = median = mode
  • Bi-modal
    • Distribution has two humps (each being a relative mode)
    • If symmetrical, mean = median
  • Skewed  
    • Positive Skew
      • Asymmetrical with tail trailing off to right
      • Mean > median > mode  
    • Negative Skew
      • Asymmetrical with tail trailing off to left
      • Mean < median < mode
    • Mean very sensitive to skew 
    • Median somewhat resistant to skew
    • Mode very resistant to skew

Characteristics of the Normal Distribution
  • Defined entirely by two parameters
  • Mean (µ)
    • Standard deviation (σ)
  • A certain percentage of all observations will always fall within +/- certain standard deviations of the mean 
    • +/- 1 Standard deviation = 68% 
    • +/- 2 Standard deviations = 95%   
    • +/- 3 Standard deviations = 99.7%
 
 

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Questions (12)
Lab Values
Blood, Plasma, Serum Reference Range
ALT 8-20 U/L
Amylase, serum 25-125 U/L
AST 8-20 U/L
Bilirubin, serum (adult) Total // Direct 0.1-1.0 mg/dL // 0.0-0.3 mg/dL
Calcium, serum (Ca2+) 8.4-10.2 mg/dL
Cholesterol, serum Rec: < 200 mg/dL
Cortisol, serum 0800 h: 5-23 μg/dL //1600 h:
3-15 μg/dL
2000 h: ≤ 50% of 0800 h
Creatine kinase, serum Male: 25-90 U/L
Female: 10-70 U/L
Creatinine, serum 0.6-1.2 mg/dL
Electrolytes, serum  
Sodium (Na+) 136-145 mEq/L
Chloride (Cl-) 95-105 mEq/L
Potassium (K+) 3.5-5.0 mEq/L
Bicarbonate (HCO3-) 22-28 mEq/L
Magnesium (Mg2+) 1.5-2.0 mEq/L
Estriol, total, serum (in pregnancy)  
24-28 wks // 32-36 wks 30-170 ng/mL // 60-280 ng/mL
28-32 wk // 36-40 wks 40-220 ng/mL // 80-350 ng/mL
Ferritin, serum Male: 15-200 ng/mL
Female: 12-150 ng/mL
Follicle-stimulating hormone, serum/plasma Male: 4-25 mIU/mL
Female: premenopause: 4-30 mIU/mL
midcycle peak: 10-90 mIU/mL
postmenopause: 40-250
pH 7.35-7.45
PCO2 33-45 mmHg
PO2 75-105 mmHg
Glucose, serum Fasting: 70-110 mg/dL
2-h postprandial:<120 mg/dL
Growth hormone - arginine stimulation Fasting: <5 ng/mL
Provocative stimuli: > 7ng/mL
Immunoglobulins, serum  
IgA 76-390 mg/dL
IgE 0-380 IU/mL
IgG 650-1500 mg/dL
IgM 40-345 mg/dL
Iron 50-170 μg/dL
Lactate dehydrogenase, serum 45-90 U/L
Luteinizing hormone, serum/plasma Male: 6-23 mIU/mL
Female: follicular phase: 5-30 mIU/mL
midcycle: 75-150 mIU/mL
postmenopause 30-200 mIU/mL
Osmolality, serum 275-295 mOsmol/kd H2O
Parathyroid hormone, serume, N-terminal 230-630 pg/mL
Phosphatase (alkaline), serum (p-NPP at 30° C) 20-70 U/L
Phosphorus (inorganic), serum 3.0-4.5 mg/dL
Prolactin, serum (hPRL) < 20 ng/mL
Proteins, serum  
Total (recumbent) 6.0-7.8 g/dL
Albumin 3.5-5.5 g/dL
Globulin 2.3-3.5 g/dL
Thyroid-stimulating hormone, serum or plasma .5-5.0 μU/mL
Thyroidal iodine (123I) uptake 8%-30% of administered dose/24h
Thyroxine (T4), serum 5-12 μg/dL
Triglycerides, serum 35-160 mg/dL
Triiodothyronine (T3), serum (RIA) 115-190 ng/dL
Triiodothyronine (T3) resin uptake 25%-35%
Urea nitrogen, serum 7-18 mg/dL
Uric acid, serum 3.0-8.2 mg/dL
Hematologic Reference Range
Bleeding time 2-7 minutes
Erythrocyte count Male: 4.3-5.9 million/mm3
Female: 3.5-5.5 million mm3
Erythrocyte sedimentation rate (Westergren) Male: 0-15 mm/h
Female: 0-20 mm/h
Hematocrit Male: 41%-53%
Female: 36%-46%
Hemoglobin A1c ≤ 6 %
Hemoglobin, blood Male: 13.5-17.5 g/dL
Female: 12.0-16.0 g/dL
Hemoglobin, plasma 1-4 mg/dL
Leukocyte count and differential  
Leukocyte count 4,500-11,000/mm3
Segmented neutrophils 54%-62%
Bands 3%-5%
Eosinophils 1%-3%
Basophils 0%-0.75%
Lymphocytes 25%-33%
Monocytes 3%-7%
Mean corpuscular hemoglobin 25.4-34.6 pg/cell
Mean corpuscular hemoglobin concentration 31%-36% Hb/cell
Mean corpuscular volume 80-100 μm3
Partial thromboplastin time (activated) 25-40 seconds
Platelet count 150,000-400,000/mm3
Prothrombin time 11-15 seconds
Reticulocyte count 0.5%-1.5% of red cells
Thrombin time < 2 seconds deviation from control
Volume  
Plasma Male: 25-43 mL/kg
Female: 28-45 mL/kg
Red cell Male: 20-36 mL/kg
Female: 19-31 mL/kg
Cerebrospinal Fluid Reference Range
Cell count 0-5/mm3
Chloride 118-132 mEq/L
Gamma globulin 3%-12% total proteins
Glucose 40-70 mg/dL
Pressure 70-180 mm H2O
Proteins, total < 40 mg/dL
Sweat Reference Range
Chloride 0-35 mmol/L
Urine  
Calcium 100-300 mg/24 h
Chloride Varies with intake
Creatinine clearance Male: 97-137 mL/min
Female: 88-128 mL/min
Estriol, total (in pregnancy)  
30 wks 6-18 mg/24 h
35 wks 9-28 mg/24 h
40 wks 13-42 mg/24 h
17-Hydroxycorticosteroids Male: 3.0-10.0 mg/24 h
Female: 2.0-8.0 mg/24 h
17-Ketosteroids, total Male: 8-20 mg/24 h
Female: 6-15 mg/24 h
Osmolality 50-1400 mOsmol/kg H2O
Oxalate 8-40 μg/mL
Potassium Varies with diet
Proteins, total < 150 mg/24 h
Sodium Varies with diet
Uric acid Varies with diet
Body Mass Index (BMI) Adult: 19-25 kg/m2
Calculator

(M1.ST.17) On morning labs, a patient's potassium comes back at 5.9 mEq/L. The attending thinks that this result is spurious, and asks the team to repeat the electrolytes. Inadvertently, the medical student, intern, and resident all repeat the electrolytes that same morning. The following values are reported: 4.3 mEq/L, 4.2 mEq/L, and 4.2 mEq/L. What is the median potassium value for that patient that day including the first value? Review Topic

QID: 103979
1

4.2 mEq/L

15%

(5/33)

2

4.25 mEq/L

73%

(24/33)

3

4.3 mEq/L

3%

(1/33)

4

4.65 mEq/L

6%

(2/33)

5

1.7 mEq/L

0%

(0/33)

M1

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(M1.ST.67) A clinical trial investigating a new biomedical device used to correct congenital talipes equinovarus (club foot) in infants has recently been published. The study was a preliminary investigation of a new device and as such the sample size is only 20 participants. The results indicate that the new biomedical device is less efficacious than the current standard of care of serial casting (p < 0.001), but the authors mention in the conclusion that it may be due to a single outlier--a patient whose foot remained uncorrected by the conclusion of the study. Which of the following descriptive statistics is the least sensitive to outliers? Review Topic

QID: 103884
1

Mean

0%

(0/15)

2

Median

20%

(3/15)

3

Mode

53%

(8/15)

4

Standard deviation

20%

(3/15)

5

Variance

7%

(1/15)

M1

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(M1.ST.19) A study on cholesterol levels of a town in rural Idaho is performed, of which there are 1000 participants. It is determined that in this population, the mean LDL is 200 mg/dL, with a standard deviation of 50 mg/dL. If the population has a normal distribution, how many people have a cholesterol less than 300 mg/dL? Review Topic

QID: 102598
1

680

6%

(2/31)

2

925

0%

(0/31)

3

950

23%

(7/31)

4

975

61%

(19/31)

5

997

3%

(1/31)

M1

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(M1.ST.69) A case series is published on the duration of symptoms in children presenting to their primary medical doctor with suspected viral upper respiratory infection. Figure A is presented in the article. What is mean, median, and mode of the duration of symptoms in this case series? Review Topic

QID: 103886
FIGURES:
1

Mean 8, median 7, mode 9

43%

(12/28)

2

Mean 7, median 5, mode 13

11%

(3/28)

3

Mean 8, median 8, mode 9

29%

(8/28)

4

Mean 7, median 8, mode 9

4%

(1/28)

5

Not enough information provided.

4%

(1/28)

M1

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(M1.ST.66) You are conducting a study on hypertension for which you have recruited 60 African-American adults. If the biostatistician for your study informs you that the sample population of your study is approximately normal, the mean systolic blood pressure is 140 mmHg, and the standard deviation is 7 mmHg, how many participants would you expect to have a systolic blood pressure between 126 and 154 mmHg? Review Topic

QID: 103883
1

10 participants

6%

(10/171)

2

41 participants

17%

(29/171)

3

57 participants

63%

(107/171)

4

68 participants

4%

(7/171)

5

Not enough information provided.

6%

(11/171)

M1

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