141-8-3-514

141-8-3-514 - Section 8.3 Variance and Standard Deviatiﬂn...

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Unformatted text preview: Section 8.3: Variance and Standard Deviatiﬂn Example: Find the mean and median of those data sets. A) 40.41140, 100. 100, 100 m (in : 7 o {Adria :’ 70 B} 60. 65. 65. 70, T5, '75, 80 Deﬁnition: The standard deviation of a data set is the measure of how V the data is spread about its mean. The variance of a data set is the average of the square of the distance from 1e Mean. t1 dt t sums H77 (SUN)?- Sample Population Notation: 8 st. deviation 0 3 b 6' /) T mean it e 1Variance : (m1 _ “l2 + [\$2 — £le + + (in — “lg '71 — {:21 —T}2 + {:32 —f)2 + + (3:...1 —s}2 71—1 Sample 1Jarianee formula : Via" Example: Compute the standard deviation and the varianee. 7 9 12 15 DP‘J’E" | ‘ | p a 9 ‘7 10 data freq. c!" 7. 3JV23 V“ = 62 : (LP/23):: 63712! Example: Compute the standard deviation and the variaiiee. Let X = the number of Dr. Peppers drank during a semester. K 10 23 43 26 250 SW]; freq. 50 30 49 T3 1 S" : 14.55547 Vif= (347': 332,5'2279‘9 Example: Compute the standard deviation. data 1 3 8 10 prob. 0.3 0.2 0.4 0.1 6“ = 3.4””: Example: Let X be a discrete random variable with integer values such that U E X E 90. The random variable has an expected value of 15.3 and standard deviation of 3. 563. A) 1Vii-That values of X are within 1.25 standard deviations of the mean? \—4——-———]‘}_ Jun-Mic J“ IHJ" ,u-rmrc a H.1r38 ,' ,o’r‘ 3 454214444— .F'K‘ an AH" Chebyshev‘s Inequality: Let X be a random variable with mean it and standard deviation 0. Then the probability that X will be Within k standard deviations of the mean is 1 Example: The random variable X has a moan of 50 and a standard deviation of 1:1. Estilnatc nun—v J.— - :{D PXg. ? I“(%)2 - .§| :15”, \$0 + KM): 7b WK: 7° r5 0“. . Example: The expected lifetime of a product is 2 years with a standard devi— ation of 3.5 months. For a, shipment of 5000 items, estimate the number of item} that will last between 17.? months and 30.3 months. I - P0115— xssvﬂ 9 "W ' "m’ ,«f Kev : 30-3 51ml. WV): 345'? 2“ mm :9-3 3-!!! 2' L3 "3 L3- 51.8 :5 ...
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141-8-3-514 - Section 8.3 Variance and Standard Deviatiﬂn...

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