Introduction to department of mathematics statistics:
Statistics is one of the main sub divisions in the applied mathematics, which deals with the scientific analysis of data. The name statistics is used for both the singular and plural sense. When used in the singular sense, it is referred to the subject as a whole. But it can be used in the plural sense, which means that it is a collection of numerical facts. The term statistics is came into existence in the middle of 18th century. Here we are going to see about the statistical determination of data and the example problems related to it.
Department of Mathematics Statistics:
Concepts in statistics:
Mean:
Mean is defined as, it is used to find the average of the total given numbers. Take the sum to all the values in the given data set and divide it by total value of the given number.
Formula for mean is,
‘barx =( sumx)/n’
Median:
Median is defined as, it is the middle value of the total given values.
If the given total value is even then the median is average of middle two values.
If the given total value is odd then the median is the middle value.
Mode:
Mode is defined as, the more number of times the value is repeated in the given data set.
Variance:
Variance is defined as the summation of the squared mean difference divided by the total number of given values.
Formula for Variance is,
S2 ='((sum(x – barx))) / (n-1)’
Standard deviation:
Standard Deviation is defined as, the total square root to the summation of the squared mean difference divided by the total number of given values.
Standard deviation is nothing but the square root of variance.
Formula for standard deviation is,
S =’ sqrt(((sum(x – barx))) / (n-1))’
Example Problems for Department of Mathematics Statistics:
Department of mathematics statistics – Problem 1:
Calculate the mean median mode for the given data set. 7, 3, 6, 2, 7, 8, 9.
Solution:
Mean: Formula for finding mean is,
‘barx =( sumx)/n’
‘barx = (7+ 3+ 6+ 2+7+ 8+ 9)/(7)’
‘”barx = 42 / 7’
‘ barx = 6’
Median: The given total values are odd so that the middle value is median.
Arrange the given data set in ascending order. 2,3,6,7,7,8,9
Median = 7
Mode: More number of times number is repeated is called mode
Here the number 7 is repeated more times .
Mode = 7
Department of mathematics statistics – Problem 2:
Find the mean, Variance and standard deviation for the following data values. ‘5400, 5500, 5450 , 5425’
Solution:
Mean: Formula for finding mean is,
‘barx =( sumx)/n’
‘barx = (5400+5500+5450+5425) / 4 ‘
‘barx = 21775 / 4’
‘barx = 5443.75’
Variance: Formula for finding variance,
S2 = ‘((sum(x – barx))) / (n-1)’
S2 = ‘((5400-5443.75)^2+(5500-5443.75)^2+(5450-5443.75)^2+(5425-5443.75)^2)/(4-1) ‘
S2 = ‘5468.75 / 3’
S2 = 1 822.91667
Standard Deviation: Formula for standard deviation is,
S =’ sqrt((sum(x)) /(n-1))’
S = ‘sqrt(5468.75 / 3)’
S = ‘sqrt( 1 822.91667)’
S = 42.6956282
Department of Mathematics Statistics – Practice Problems:
1. Calculate the mean median mode for the given data. 23, 34, 12, 45, 23.
Answer: ‘barx ‘ = 27.4
Median = 23
Mode = 23
2.Find the variance and standard deviation for the following. 2,3,4,5,6
Answer: mean = 4
Variance = 2.5
Standard Deviation = 1.5811388300842
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