Statics is most popular and important topic in the mathematics. It is commonly used for finding the Mean, Mode and Median for a set of data, to compute Range, Variance and Standard Variation and also help us to understand the means of these. We construct the Box and Whiskers plot with the help of the statics. It creates capable us to compute the Coefficient of Variation and z scores. We also calculate the Center and Location, Weighted mean, Percentiles, Quartiles and other measures of locations. We use the numerical measures along with graph, charts and tables to describe data. So in this way we can say that Statics is a way to describe the data.
Measurement of Center and Location
There are four ways for finding Center and Location.
(i) Mean,
(ii) Mode,
(iii) Median and
(iv) Weighted mean.
(i) Mean: - It is the arithmetic average of data value. Mean is “the sum of the values divided by the number of the values”.
e.g., we have to find the mean of the values 1,2,3,4 and 5.
Then mean of the given numbers = sum of the values/no. of values
= (1+2+3+4+5)/5 = 3
It is of two types, they are-
Sample mean: -
where n is the number of terms in the sample.
Population mean: -
where N is the number of terms in the population.
(ii) Mode : - A measure of the central tendency and the value which occurs most often is called ‘Mode’.
e.g., the number of marks obtained in a exam of Statics is listed below. Which score occurred most often or find the mode?
7, 13, 18, 24, 9, 3, 18
Solution: - Ordering the scores from least to greatest, we get:
3, 7, 9, 13, 18, 18, 24
So, the mark which occurs most often is 18.
(iii) Median: - Median is the ‘middle value’ of the ranked data.
e.g., find the median for the following list of the values.
3, 8, 3, 4, 3, 6, 4, 2, 3
Solution: - The median is the middle value, so we'll have to rewrite the list in order:
3, 3, 3, 3, 4, 4, 6, 8, 2
There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number. So the median is 4.
Note: - If the number of the values is even then the median will the mean of the middle two values.
(iv) Weighted mean: - It is used when values are grouped by frequency or relative importance.
e.g., Sample of 26 repair projects:
Days to complete | Frequency |
5 6 7 8 | 4 12 8 2 |
=164/26=6?31 days.
Percentile,quartiles and Range
v) Percentile:- In an ordered array of n value is given then pth percentile in nth position is determined as following formula:
e.g.,- the 60th percentile in an ordered array of 19 values is the value in 12th position:
Solution: - n = p(N+1)/100 = 60(19+1)/100 = 12
vi) Quartiles: - It split the ranked data into 4 equal groups i.e., it creates 4 groups of the array, that means it creates the division of data array in 4 equal parts. So each of the Quartile is of 25%.
e.g.- find the first Quartile for the given sample of data
11 12 13 16 16 17 18 21 22
Solution:-Here number of values n=9
So the first quartile Q1= 25th percentile, so 25th percentile of the data
=25(9+1)/100 = 2?5 position
So use the value half way between 2nd and 3rd values, so Q1=12?5
vii) Range:-The range may be defined as a difference between the largest and the smallest value in the given data list.
Range= Xmax ? Xmin
e.g., Find the range of the given data array:
7 8 9 10 11 12 13
Solution:- Range = Xmax?Xmin = 13?7 = 6
viii) Box and whisker plot: -
It is very useful and used to handling many data values. It is also known as “ Five number summary”. It consists of the means, two quartiles, the smallest and greatest value in the distributions. Median divides the data in two halves and the quartile divides the data between these two halves, so it is called sub-median.
Related Tags
Explain Data Using Statistics , Notes on Data Using Statistics , Data Using Statistics online notes