bio-statistics, measures of central tendency, measures of dispersion, mean, median, mode, slandered deviation, variance, range

1. BIOSTATISTICS
Part 2
Data interpretation
Dr. noorah murad
B.D.S. D.D.S.
LECTURE 13
BIOSTATISTICS

2. Two kinds of statistics are frequently used to
describe data:
1. Measures of central tendency.‫المركزية‬ ‫النزعه‬
 mean ‫المعدل‬
 Median ‫الوسيط‬
 Mode ‫تكرار‬ ‫االكثر‬ ‫القيمه‬
2. Measures of dispersion.‫التشتت‬ ‫مقياس‬
• Standard deviation ‫المعياري‬ ‫االنحراف‬
• Variance ‫التباين‬
• Range ‫المدى‬
DATA DESCRIPTION

3.  Define as: A score that indicate where the center of
description tend to be located.
 Presented as: A single value describe a set of data by
identifying the central position of distribution within that
set.
Purpose:
1. They help summarize a lot of scores with a single
number.
2. they give idea about the shape and nature of
distribution.
MEASURES OF CENTRAL TENDENCY

4. Mean
(or average )
Equals to the sum
of all values in the
data set divided by
the number of
values in the data
set
Mode
The most
frequent score in
a data set
CENTRAL TENDENCY MEASURES
Median
The middle value of
a set of data that has
been arranged in
order of magnitude
Half data are above
and half are below
the median

5. Example:
MEAN : 𝑥 n= ‫القيم‬ ‫عدد‬
𝑥 =
𝑥1+𝑥2+𝑥3…𝑋12
𝑛
𝑥 =
6+5+8+2+3+4+5+9+7+14+12
11
MEASURES OF CENTRAL TENDENCY
1214795432856
X12X10X9X8X7X6X5X4X3X2X1

6. MEASURES OF CENTRAL TENDENCY
Median : number of scores Odd ‫فردي‬
Median : number of scores Even ‫زوجي‬
Median =
5+6
2
= 5.5
1412987655432
12987655432

7. Mode : most frequent data
Mode : 5
MEASURES OF CENTRAL TENDENCY
1214795432856

8. Is a numerical value describing the amount of
variability present in a data set.
It helps in describing the spread of scores
within a group of scores
(if the scores are close together or if they are
far apart from each other)
MEASURES OF DISPERSION

9.  We measure dispersion of data either by one of the
followings:
Standard deviation
Variance
range H – L where H: largest value
L: smallest value
MEASURES OF DISPERSION

10.  Most commonly used measure of dispersion.
 It is used to quantify the amount of variation or dispersion of
a set of data values.
 Low standard deviation indicate that the data points tend to
be close to the mean.
 A high standard deviation indicate that the data points are
spread out over a wider range of values.
 Measure the scatter of the values about their mean.
It is the square root of the variance
STANDARD DEVIATION SD

11. Measures the degree of spread in a
variable’s values.
If the data tend to be far away from the
mean, the variance will be large.
If the data tend to be close to the mean, the
variance will be small.
It is the square of standard deviation
VARIANCE

12. 1. Calculate the mean. 𝑥
2. Write a table that subtracts the mean from each
observed value. X- 𝑥
3. Square each of the differences. (x- 𝑥)2
4. Summation of the (x- 𝑥)2
5. Divide by n-1 where n is the number of items in
the sample.
this is the variance
 to get the SD we take the square root of the
variance
STEPS TO CALCULATE VARIANCE
AND SD

13. • Range: is defined as the difference between the
largest and the smallest values in a data set
• Affected by just one unusually large or small
value.
range H – L where H: largest value
L: smallest value
SD, VARIANCE AND RANGE