Updated: 8/5/2018

# Statistical Distribution

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Review Topic
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Questions
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Evidence
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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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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: 5-23Â Î¼g/dL //1600 h: 3-15 Î¼g/dL 2000 h: â‰¤ 50% of 0800 h Creatine kinase, serum Male: 25-90 U/LFemale: 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/mLFemale: 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/dL2-h postprandial:<120 mg/dL Growth hormone - arginine stimulation Fasting: <5 ng/mLProvocative 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 Î¼g/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 30Â° 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 .5-5.0Â Î¼U/mL Thyroidal iodine (123I) uptake 8%-30% of administered dose/24h Thyroxine (T4), serum 5-12 Î¼g/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/mm3Female: 3.5-5.5 million mm3 Erythrocyte sedimentation rate (Westergren) Male: 0-15 mm/hFemale: 0-20 mm/h Hematocrit Male: 41%-53%Female: 36%-46% Hemoglobin A1c â‰¤ 6 % Hemoglobin, blood Male: 13.5-17.5 g/dLFemale: 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 80-100Â Î¼m3 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/kgFemale: 28-45 mL/kg Red cell Male: 20-36 mL/kgFemale: 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/minFemale: 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 hFemale: 2.0-8.0 mg/24 h 17-Ketosteroids, total Male: 8-20 mg/24 hFemale: 6-15 mg/24 h Osmolality 50-1400 mOsmol/kg H2O Oxalate 8-40 Î¼g/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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PREFERRED RESPONSE 2
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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%

(0/27)

2

Median

19%

(5/27)

3

Mode

52%

(14/27)

4

Standard deviation

19%

(5/27)

5

Variance

4%

(1/27)

M1

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PREFERRED RESPONSE 3
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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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PREFERRED RESPONSE 4

(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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PREFERRED RESPONSE 1
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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%

(10/179)

2

41 participants

18%

(32/179)

3

57 participants

62%

(111/179)

4

68 participants

4%

(8/179)

5

Not enough information provided.

6%

(11/179)

M1

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PREFERRED RESPONSE 3
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