A fast bowler delivered 30 overs (180 deliveries) out of which the speeds of his 24 overs (144 deliveries) 122 124 124 125 126 126 126 127 127 127 127 128 128 129 129 129 129 130 130 130 131 131 131 131 131 131 131 131 132 132 132 132 132 132 132 132 132 132 133 133 133 133 133 133 133 133 133 133 133 133 133 133 133 134 134 134 134 134 134 134 134 134 134 134 134 134 134 134 134 134 134 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 136 136 136 136 136 136 136 136 136 136 136 136 137 137 137 137 137 138 138 138 138 138 138 138 138 139 139 139 139 139 139 140 140 140 140 140 140 141 141 141 141 142 143 143 143 143 143 144 144 144 144 145 145 a) Use this data to construct a frequency distribution with suitable number of classes. b) Construct a Histogram and O-give using your constructed frequency distribution. c) Calculate the Arithmetic Mean and Mode for the given data (For Grouped Data). d) Calculate the sample variance and standard deviation for the given data (For Grouped Data). e) Using columns of Class limits and frequency of your constructed distribution find: i. All the quartiles ii. 4th and 8th Deciles
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A fast bowler delivered 30 overs (180 deliveries) out of which the speeds of his 24 overs (144
deliveries)
122 124 124 125 126 126 126 127 127
127 127 128 128 129 129 129 129 130
130 130 131 131 131 131 131 131 131
131 132 132 132 132 132 132 132 132
132 132 133 133 133 133 133 133 133
133 133 133 133 133 133 133 133 134
134 134 134 134 134 134 134 134 134
134 134 134 134 134 134 134 134 135
135 135 135 135 135 135 135 135 135
135 135 135 135 135 135 135 135 135
135 136 136 136 136 136 136 136 136
136 136 136 136 137 137 137 137 137
138 138 138 138 138 138 138 138 139
139 139 139 139 139 140 140 140 140
140 140 141 141 141 141 142 143 143
143 143 143 144 144 144 144 145 145
a) Use this data to construct a frequency distribution with suitable number of classes.
b) Construct a Histogram and O-give using your constructed frequency distribution.
c) Calculate the Arithmetic Mean and
d) Calculate the sample variance and standard deviation for the given data (For Grouped Data).
e) Using columns of Class limits and frequency of your constructed distribution find:
i. All the
ii. 4th and 8th Deciles
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