The test scores on a 100-point test were recorded for 20 students. 61 92 93 85 54 74 87 81 77 96 93 89 99 91 96 76 83 73 88 67 (a) Use a stem and leaf plot to describe the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) 5 6 17 3467 8. 135780 9. 1233669 (b) Describe the shape and location of the scores. O The distribution is bimodal. O The distribution is skewed to the right. O The distribution is mound shaped. O The distribution is skewed to the left. (c) Is the shape of the distribution unusual? Can you think of any reason that the scores would have such a shape? O The shape is not unusual and could be indicative of an extremely difficult test in which most students performed poorly. O The shape is not unusual and could be indicative of a typical test in which most students scored around the average with a few students performing poorly and a few students performing very well. • The shape is not unusual and could be indicative of two distinct groups of students those who understand the material and those who don't. O The shape is not unusual and could be indicative of an easy test in which most students performed very vell, O The shape is highly unusual and is probably indicative of errors in the writing of the test since none of the students performed well.
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.
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