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S_A_V [24]
3 years ago
15

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider

the following data set.4, 4, 5, 8, 12(a) Compute the mode, median, and mean.i. mode ii. median iii. mean (b) Multiply each data value by 6. Compute the mode, median, and mean.i. mode ii. median iii. mean (c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant?Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c.Multiplying each data value by the same constant c results in the mode, median, and mean remaining the same. Multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c.There is no distinct pattern when each data value is multiplied by the same constant.(d) Suppose you have information about average heights of a random sample of airline passengers. The mode is 68inches, the median is 70 inches, and the mean is 70 inches. To convert the data into centimeters, multiply each data value by 2.54. What are the values of the mode, median, and mean in centimeters? (Enter your answers to two decimal places.)i. mode cmii. median cmiii. mean cm
Mathematics
1 answer:
andreev551 [17]3 years ago
6 0

Answer:

a) Mean = 4.6, median = 3, mode =2

b) Mean = 13.8, median = 9, mode = 6

c) Option C) Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c

Step-by-step explanation:

We are given the following data:

2, 2, 3, 6, 10

a) Mean, median and mode

Sorted data: 2, 2, 3, 6, 10

Mode is the most frequent observation in data.

Mode = 2

b) Multiplying data set by 3

6, 6, 9, 18, 30

Mode = 6

C) Comparison

The mean, median and mode of the new data increased by a factor of 3.

Option C) Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c

Click to let others know, how helpful is it

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xxMikexx [17]

Answer:

450 x 15 = 6750 ft 2

Step-by-step explanation:

6 0
3 years ago
Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
nataly862011 [7]

Let (<em>x</em>, <em>y</em>, <em>z</em>) be a point on the plane in the first octant. The box formed by this point has volume <em>xyz</em>, and you want to maximize this subject to the equation of the plane.

Use the method of Lagrange multipliers: the Lagrangian is

<em>L</em>(<em>x</em>, <em>y</em>, <em>z</em>) = <em>xyz</em> - <em>λ</em> (<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6)

Find its critical points:

∂<em>L</em>/∂<em>x</em> = <em>yz</em> - <em>λ</em> = 0

∂<em>L</em>/∂<em>y</em> = <em>xz</em> - 2<em>λ</em> = 0

∂<em>L</em>/∂<em>z</em> = <em>xy</em> - 3<em>λ</em> = 0

∂<em>L</em>/∂<em>λ</em> = -(<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6) = 0

Solving the first three equations for <em>λ</em> gives

<em>λ</em> = <em>yz</em> = <em>xz</em>/2 = <em>xy</em>/3

Solve these equations for <em>y</em> and <em>z</em> :

• <em>yz</em> = <em>xz</em>/2   =>   <em>y</em> = <em>x</em>/2   =>   2<em>y</em> = <em>x</em>

• <em>yz</em> = <em>xy</em>/3   =>   <em>z</em> = <em>x</em>/3   =>   3<em>z</em> = <em>x</em>

Substitute these solutions into the last equation and solve for <em>x</em>, then again for <em>y</em> and <em>z</em> :

<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6 = 3<em>x</em> - 6 = 0   =>   3<em>x</em> = 6   =>   <em>x</em> = 2, <em>y</em> = 1, <em>z</em> = 2/3

At this critical point, the maximum volume is

<em>xyz</em> = 2*1*2/3 = 4/3

4 0
3 years ago
A random sample of 84 students at a university showed an average age of 22 years and a sample standard deviation of 3 years. Fin
Debora [2.8K]

Answer:

The margin of error for the 94% confidence interval is 0.6154.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population mean is:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The margin of error of this interval is:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The critical value of <em>z</em> for 94% confidence level is, <em>z</em> = 1.88.

Compute the margin of error for the 94% confidence interval as follows:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

          =1.88\times\frac{3}{\sqrt{84}}\\\\=0.6154

Thus, the margin of error for the 94% confidence interval is 0.6154.

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andre [41]
The answer to this is x < -10/7
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