lecture 2 biostats

Mode

Most frequently occurring value

not good summary of database

Median

Middle value wen the sample size is odd

even sample size : average of two middle values

Mean

Arithmetic average of values

Two limitations with mode

May contain scores that are all tied at the same highest frequency

rectangular distribution ( each number has same frequency)

mode is a score of category NOT a ___

mode is a score of category NOT a Frequency

Model class is the class with the largest___

Model class is the class with the largest Frequency

Parameter

Numerical fact about population

Statistics

Number calculated from sample

Mean as balance point : what’s meant by balance ?

Sum of deviations from mean to the left balance out the sum of the deviations from the mean to the right

calculate weighted mean

(Sigma)X1+(sigma)X2/(n1+n2)

(Sigma)X- overall sum of scores in each group

N-total number of scores in each group

Calculate median

(n+1)/2th largest value odd

(n/2)th,(n+2)/2

unimodal symmetric distribution

Biomedical symmetric distribution

Rectangular distribution

Positive skewed

mode<mdn<mean

Negative skewed distribution

mean<median<mode

pros n cons mean

+ best for symmetrical data

+best for large datasets

-easily thrown off by outliers

pros n cons median

+best for asymmetrical data

+easy to find

-not useful for qualitative data

pros n cons Mode

+best for qualitative data

+easy to find

-multiple modes

Variability (or dispersion)

extent data points in dataset differ from each other and from the central tendency

Measured spread or distribution of data values

higher variability indicates a __ spread of data

higher variability indicates a wide spread of data

lower variability data points are more ___ around the mean

values in dataset more consistent

lower variability data points are more clustered around the mean

range

Diff btwn max and min values

max values - min value

Susceptible to outliers

interquartile range (IQR)

Spread of the middle 50% of data

calculated as

IQR= Q3-Q1

Q3-75th percentile

Q1-25th percentile

Variance (o² or s²)

Average of the squared differences from the mean

deviation calculation

Xi-X(sum) = Xi - M

Standard deviation

Square root of variance giving a measure of spread in the same units as the data

Unimodel symmetric distribution following holds

68% distribution lie within one standard deviation of mean

95% distribution lie within two standard deviation of mean

99.7% lies within three standard deviation of the mean

coefficient of variation (CV)

Alternate way to measure variation

VC expressed the standard deviation as a

expressed standard deviation as percentage or ratio of the mean

The higher the CV greater variability about the mean

The lower the CV more consistent individuals are about the mean

Modal class

Class with largest frequencies