That number is called the variance of the series of numbers; the is a key concept in statistics; variance it is good for you to understand well how it is obtained, and to understand that a) the larger the differences between the numbers in the series, the higher the variance of that series b) one large difference may contribute more to the size of the variance than several small differences together. The square 8.75² (76,56), for example, contributes more to the size of the variance than 6 other squares together 0,75² + 3,75² + 0,75² + 5,25² + 0,25² + 2,25² = 47,88. Just remember this for a while, until we mention the squares principle’ ‘least c) if all measured heights would be equal, the variance would become zero. That should be obvious: if all the numbers are equal, there is no in them ‘variance’ Finally, to obtain a number for the difference’, ‘typical a number better comparable to a difference than to a squared difference, we the variance by taking its square root, i.e. ‘un-square’ 20,43751/2 = 4,52 cm. This number, this deviation’ ‘average is called the deviation’ (or difference’) ‘standard ‘typical of the series of numbers. Within our group of children, the standard deviation of the heights is 4,52 cm. If we take any child at random, and ask ourselves how much we can expect its height to differ from the average in its group?” “by the answer would be by 4.52 cm”. “typically We see that the first child’s height is less (0,75) than one typical difference above the mean height; it is rather average in height. The fifth child lies about two deviations’ above the mean (8,75); . ‘standard it can safely be called taller’ relative to its group. ‘much The sixth child is more than one standard deviation below the mean (-6,25); it is smaller. In computing the standard deviation, an important statistical number by itself, we have illustrated the use of squaring values, of summing squares and of taking the square root.
That number is called the variance of the series of numbers; the variance is a key concept in statistics; it is good for you to understand well how it is obtained, and to understand that a) the larger the differences between the numbers in the series, the higher the variance of that series b) one large difference may contribute more to the size of the variance than several small differences together. The square 8.75² (76,56), for example, contributes more to the size of the variance than 6 other squares together 0,75² + 3,75² + 0,75² + 5,25² + 0,25² + 2,25² = 47,88. Just remember this for a while, until we mention the ‘least squares principle’ c) if all measured heights would be equal, the variance would become zero. That should be obvious: if all the numbers are equal, there is no ‘variance’ in them Finally, to obtain a number for the ‘typical difference’, a number better comparable to a difference than to a squared difference, we ‘un-square’ the variance by taking its square root, i.e. 20,43751/2 = 4,52 cm. This number, this ‘average deviation’ is called the ‘standard deviation’ (or ‘typical difference’) of the series of numbers. Within our group of children, the standard deviation of the heights is 4,52 cm. If we take any child at random, and ask ourselves “by how much we can expect its height to differ from the average in its group?” the answer would be “typically by 4.52 cm”. We see that the first child’s height is less (0,75) than one typical difference above the mean height; it is rather average in height. The fifth child lies about two ‘standard deviations’ above the mean (8,75); . it can safely be called ‘much taller’ relative to its group. The sixth child is more than one standard deviation below the mean (-6,25); it is smaller. In computing the standard deviation, an important statistical number by itself, we have illustrated the use of squaring values, of summing squares and of taking the square root.
TOPICOS%20EXAMEN%20PRAG-MATEMATICAS%202017.docx