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3 years ago

28, 45, 12, 34, 36, 45, 19,20

Mathematics

1 answer:

arlik [135]3 years ago

6 0

Part A

To find the mean, we add up the values and divide by n = 8 since there are 8 values in this set.

Adding the values gets us

28+45+12+34+36+45+19+20 = 239

Dividing this over 8 then leads to 239/8 = 29.875

<h3>Answer: 29.875</h3>

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Part B

We'll subtract each data value from the mean. We apply absolute value to ensure the result is never negative.

|28 - 29.875| = 1.875
|45 - 29.875| = 15.125
|12 - 29.875| = 17.875
|34 - 29.875| = 4.125
|36 - 29.875| = 6.125
|45 - 29.875| = 15.125
|19 - 29.875| = 10.875
|20 - 29.875| = 9.875

The list of results we get so far is:

1.875, 15.125, 17.875, 4.125, 6.125, 15.125, 10.875, 9.875

This represents the distance each value is from the mean.

Add these values up and divide by n = 8

1.875+15.125+17.875+4.125+6.125+15.125+10.875+9.875 = 81

81/8 = 10.125

<h3>Answer: 10.125</h3>

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Part C

The result of part A is one way to measure the center of the distribution of values. It's the average value, which can more or less represent the entire group. Think of it being like how people vote in a senator to represent them in congress. Ideally, this senator is a supposed "average" person to represent everyone.

The result of part B builds on what part A found. The result of part B is the average distance each value is from the center. This is because each time we subtracted and applied absolute value, we found the distance that item was from the mean.

Example: The calculation |28 - 29.875| = 1.875 shows that 28 is exactly 1.875 units from the mean 29.875

By adding up those results and dividing by 8, we are finding the average distance from the mean. Effectively, it tells us how spread out the data set is. The mean absolute deviation (MAD) is a measure of spread in a similar fashion that the standard deviation is, or in a more looser sense, the range is as well.

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In short, the result of part A is a measure of center while the result of part B is a measure of spread. I use "a" instead of "the" because there are other measures of center and other measures of spread.

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natita [175]

Answer:

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Step-by-step explanation:

<u>The correct question is:</u> The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?

Let X = <u>playing time of jazz CDs</u>

SO, X ~ Normal( $\mu=52, \sigma^{2} =7$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, according to the 68-95-99.7 rule, it is stated that;

68% of the data values lie within one standard deviation points from the mean.

95% of the data values lie within two standard deviation points from the mean.

99.7% of the data values lie within three standard deviation points from the mean.

Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;

For 45 minutes, z-score is = $\frac{45-52}{7}$ = -1

For 59 minutes, z-score is = $\frac{59-52}{7}$ = 1

This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.

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