Variance and Standard deviation

Variance and Standard deviation: Theory - Exercises
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We throw a dice $$10$$ times consecutively, obtaining the results: $$1, 1, 1, 3, 3, 4, 4, 5, 6, 6$$. Calculate the variance and the typical deviation of the throws.

Variance and Standard deviation: Theory - Exercises
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The same exam is given to all the first grade classes in a high school. The teachers from the three classes of $$30$$ students each agree that, when correcting, they will get the same average.

Standard deviations of the grades of each class are, respectively $$\sigma_1=2,45$$; $$\sigma_2=3,21$$ and $$\sigma_3=2,78$$. Find the typical deviation of the total marks of the exam.

Variance and Standard deviation: Theory - Exercises
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The teacher of mathematics allows each student to choose the exercise that he or she prefers from the 4 exercises proposed in the examination. The teacher guarantees the student that the average of the grades in each exercise will be the same. The results are the followings:

  • $$15$$ pupils choose exercise $$1$$, whereby standard deviation of the grades turns out to be $$\sigma_1=2,73$$.
  • $$4$$ pupils choose exercise $$1$$, whereby standard deviation of the grades turns out to be $$\sigma_2=1,22$$.
  • $$9$$ pupils choose exercise $$1$$, whereby standard deviation of the grades turns out to be $$\sigma_3=3,12$$.
  • $$3$$ pupils choose exercise $$1$$, whereby standard deviation of the grades turns out to be $$\sigma_4=2,87$$.

Find the variance and the typical deviation of the marks of the whole class.

Variance and Standard deviation: Theory - Exercises
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Next, the points of a basketball team are shown. Find the existing typical deviation. $$$73-\mbox{PANATINAIKOS}(21+27+8+17): \\ \mbox{Spanoulis}(13), \ \mbox{Pekovic}(6), \ \mbox{Fotsis}(13), \ \mbox{Nicholas}(7), \ \mbox{Perperoglou}(6), \\ \mbox{Batiste}(6), \ \mbox{Diamantidis}(10), \ \mbox{Jasikevicius}(10), \ \mbox{Tsartaris}(2)$$$

Variance and Standard deviation: Theory - Exercises
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We have the temperatures in several cities of Spain: Aviles $$(11^\circ C)$$, Barcelona $$(17^\circ C)$$, Madrid $$(21^\circ C)$$, Mallorca $$(18^\circ C)$$, Valencia $$(18^\circ C)$$, Marbella $$(19^\circ C)$$, Las Palmas $$(20^\circ C)$$.

Calculate the typical deviation of these temperatures.