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Cara computes the mean and variance for the set 87, 46, 90, 78, and 89. She finds the mean to be 78. Her steps for finding the variance are shown below. Variance squared = StartFraction (87 minus 78) squared + (46 minus 78) squared + (90 minus 78) squared + (78 minus 78) squared + (89 minus 78) squared Over 5 EndFraction Variance squared = StartFraction (9) squared minus (32) squared +

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Answer:

The answer is 274

Step-by-step explanation:

Given;

  • Cara computes the mean and variance for the set 87, 46, 90, 78, and 89. She finds the mean to be 78.

To Find;

  • Variance:-

Now,

Definition of Variance:

  • Variance is the value of the squared variation of the random variable from its mean value, in probability and statistics.

So,

[tex] \frac{ {(87 - 78)}^{2} + ( {46 - 78)}^{2} + (90 - 78) {}^{2} + ({78 - 78)}^{2} + ( {89 - 78)}^{2} } {5} [/tex]

[tex]Var(X) \: = \frac{1370}{5} = 274 \\ [/tex]

Thus, The variance of the sequence is 274.

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