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3 years ago

Using the following data, calculate the mean absolute deviation:

Mathematics

2 answers:

mojhsa [17]3 years ago

8 0

Answer:

The mean absolute deviation of first data is $2.54$

and for second data is $2.115$

Step-by-step explanation:

Mean of data $x_1,x_2,x_3,x_4,...x_{n}$ is calculated as:

$mean=\frac{x_1+x_2+x_3+x_4+...+x_n}{n}$

and mean absolute deviation is calculated as $\sqrt{mean}$

The given first data : 10 7 1 6 7 9 8 10 2 5

$mean=\frac{x_1+x_2+x_3+x_4+...+x_n}{n}$

$mean=\frac{10+7+1+6+7+9+8+10+2+5}{10}$

$mean=6.5$

mean absolute deviation $\sqrt{6.5}=2.54$

The given first data : 2 2.4 6.5 7

$mean=\frac{x_1+x_2+x_3+x_4+...+x_n}{n}$

$mean=\frac{2+2.4+6.5+7}{4}$

$mean=\frac{17.9}{4}$

$mean=4.475$

mean absolute deviation $\sqrt{4.475}=2.115$

Therefore, the mean absolute deviation of first data is $2.54$

and for second data is $2.115$

Bogdan [553]3 years ago

3 0

First set of data:
Mean - 6.5
Absolute deviation - 2.4

Second set of data:
Mean - 4.475
Absolute deviation - 2.275

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Answer:

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Answer:

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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How likely is the resulting sample proportion to be between 0.066 and 0.294?

This is the pvalue of Z when X = 0.294 subtracted by the pvalue of Z when X = 0.066. So

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By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

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$Z = -2.97$

$Z = -2.97$ has a pvalue of 0.0015

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0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

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