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Statistics- introduction, frequency distribution, scales of measurement, presentation of data
Bsc nursing (blaw 213)
Kerala University of Health Sciences
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Year Population in million 1900 240 1910 250 1920 248 1930 280 1940 380 1950 360 1960 440 1970 550
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980
0
100
200
300
400
500
600
Population in million
II Qualitative discrete data:-
i) Bar diagram
It is convenient graphical device ie; particularly useful for displaying nominal or ordinal comparison of the magnitude of different frequencies. Length of the bar drawn vertical or horizontal that/which indicate the frequency of a character. There are three types pf bar diagram.
a. Simple bar diagram b. Multiple bar diagram c. Proportional or subdivided bar diagram.
a. Simple bar diagram
Gender Men Women Frequency 60 45
Men Women 0
10
20
30
40
50
60
70
b. Multiple bar diagram
Continents Population in million
Area
Asia 60 20 Africa 15 25 Europe 22 10 North America 5 20
Asia Africa Europe North America
0
10
20
30
40
50
60
70
Population in million Area
c. Proportional or subdivided bar diagram.
Continents Population in million
Area Population % Area %
Asia 60 20 (60/80)x 75
(20/80)x 25 Africa 15 25 (15/40)x 37.
(25/40)x 62. Europe 22 10 (22/32)x 68.
(10/32)x 31. North America 5 20 (5/25)x 20
(20/25)x 80
There are two main objectives of the study of average.
i. To get single value that describe the characteristic of the entire group. ii. To facilitate comparison. Types of Averages : - i. Arithmetic Mean ii. Median iii. Mode iv. Geometric Mean v. Harmonic Mean
i. Arithmetic Mean
The measure implies arithmetic average or arithmetic mean which is obtained by summing up all the observation and dividing the total by the number of observations.
*Calculating mean for ungrouped data: -
This is the sum of the separate scores divided by their number.
Formula of Mean (M) or () of a series of
Mean () =
Here = X 1 +X 2 +X 3 +....... Xn
= Mean
= Total
X = score
N = Number of observations
Eg:- 1. Complete the average of following set of data:
Score -> 8, 4, 5, 3, 7, 6, 3, 8, 3, 3
Mean () =
=
=
= 5
So Mean = 5
Calculate mean for grouped data
When measures have been grouped into a frequency distribution the mean is calculated by a slight different method.
i. First fx column is found by multiplying the x of each interval by the number of score. ii. Then the mean is the sum of the fx divided by N
Formula of Mean for grouped data is Mean () =
= Mean
= Sum
F = frequency
X = score
N = Number of observations
Here is grouped data N = F
- Calculate the mean for the following score
X F Fx 4 4 16 5 5 25 6 4 24 7 3 21 8 2 16 9 2 18 F =20 120
() = = = () = 6
- Calculate the mean for grouped data : -
Class interval Frequency X fx 50 - 52 13 51 663 52 – 54 12 53 636 54 - 56 16 55 880 56 – 58 14 57 798 58 - 60 13 59 767 60 - 62 15 61 915 62 - 64 17 63 1071 F =100 5730
=
=
= 57.
= 57.
- Calculate the mean for grouped data : -
Class interval Frequenc X fx
Mean of 5th and 6th position = ()
= = 5
Median = 5
- Calculate the median for the given ungrouped data? 3, 4, 3, 5, 6, 8, 5, 4, 7
Arranged in ascending order -> 3, 3, 4, 4, 5, 5, 6, 7, 8
Median = )th value
= ()th value
= 5th value.
Take the 5th position value = 5
Median = 5
- Calculate median for grouped data : -
The formula for calculating mean under grouped data
Median = L + (x
Here equals to number of score in the group divided by 2 (ie; )
L = exact lower limit of median class internal
m = frequency up to class internal in which median fall.
f = frequency at the median class interval.
w or i = number or size of the class interval.
*Steps : -
i. First divide the number of scores in the group by 2 to give the location of the median.
ii. Find the exact lower limit (L) of the class interval on which median form.
iii. Find the frequency up to the class interval on which the median fall(m).
iv. Find the frequency at the class interval on which median fall(f).
v. Apply the formula for median.
Median = L + (x
Exercise : -
- Calculate the median for the following set of frequency distribution
Marks Frequenc y
Calculative frequency
46 - 50 2 2 51 - 55 1 3 56 - 60 5 8
61 - 65 7 15
66 - 70 3 18
71 - 75 2 20
76 - 80 5 25
f = 25
i. Find median value = = = 12.
12 will include in 15th ------ frequency.
Median class = class which contains th observation ie. 61-
ii. L = lower limit of class interval ie. 61
iii. m = frequency up to the median class ie. 2+1+5 = 8
iv. f = frequency at the class intend ie. 7.
v. w= number or size of the class interval ie. 61 – 65 = 5
vi. Median = L + (x
= 61 + (x
=61 + (x
=61 + (x
=61 + (x
=61 +
= 64.
Median = 64.
- Calculate the median for the following data
Class interval frequency Comutative frequency 80 - 100 8 8 100 - 120 12 20 120 - 140 16 36 140 – 160 8 44 160 - 180 6 50
f (N)= 50
Median value = = = 25
25 th commutative frequency will include is 36
Median lass interval = class which contain th observation. ie. 120 – 140
L = 120 m = 20 f = 16 w = 20
L = lowest limit of the model of class.
F = frequency of the model of the class.
w = width of the model of class
f1= frequency of the just before the model of class
f2= frequency of the class just after the of class
Model class is the one which has the highest frequency
Exercise: -
- Calculate the mode for the following data: -
Class interval Frequency 100 - 150 5 150 - 200 19 200 - 250 3 250 - 300 11 300 - 350 6 350 - 400 9
Model class = 150 - 200
L = 150 f = 19 w = 20 f 1 = 5 f 2 = 3
Mode (Z) = L+ x w
= 150+ x 50
= 150+ x 50
= 150+ x 50
= 150+ x 50
= 150+ x 50
= 150+ = 173.
Mode of the given data = 173.
- Identify the mode in the following discrete data
X f 100 5 150 19 200 3 250 11 300 6 350 9
Z = value which has the highest frequency ie. 19 in the above table x the corresponding “x” value is 150. So, 150 is the mode.
Mode = 150
- Merits of Mode: -
i. It is not affected by extreme value.
ii. It can be used to describe the qualitative phenomenon.
iii. Values of mode can be determined graphically.
- Demerits of Mode: -
i. The value of mode cannot always be determined. It is not based on each value.
ii. It is not capable of algebraic manipulation.
- Measure of variability/Dispersion: -
It is also known as measure of variability. It helps to find new individual observations are dispersed around a mean of a large scale.
- Definition: -
Dispersion spread is the degree of the scatter or variation of the variable about a central value by Brook’s and Dick.
- Signature of measuring variation: -
Measuring of variation is needed for 4 basic purposes.
- To determine the reliability of an average.
- To serve as a basis for the control of the variability,
- To compare 2 or more series with regard to their variability.
- To facilitate the use of other statical measures.
*Properties of Good measure of variation: -
It should be simple to understand.
It should be easy to compute.
It should be rigidly defined.
It should be bases on each and every item in the distribution.
It should be useful for further statistical treatment.
It should have sampling stability.
It should not be affected by extreme items.
Methods of calculating variation: -
- Range
- Mean deviation
- Standard deviation
- Quartile deviation.
*1. Range: -
Range = 25
Co-efficient of range =
=
=
= 0.
Co-efficient of range = 0.
Statistics- introduction, frequency distribution, scales of measurement, presentation of data
Course: Bsc nursing (blaw 213)
University: Kerala University of Health Sciences
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