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Blizzard
1 month ago
6

Exercise 2.2 gave the following data (in increasing order) for the attribute age: 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25

, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70. (a) Use smoothing by bin means to smooth these data, using a bin depth of 3. Illustrate your steps. Comment on the effect of this technique for the given data. (b) How might you determine outliers in the data? (c) What other methods are there for data smoothing?
Mathematics
1 answer:
babunello [11.4K]1 month ago
7 0

Answer:

Step-by-step explanation:

Data given in ascending order: 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.

a) Smoothing via bin means:

Bins of size 3:

Bin 1: 13, 15, 16

Bin 2: 16, 19, 20

Bin 3: 20, 21, 22

Bin 4: 22, 25, 25

Bin 5: 25, 25, 30

Bin 6: 33, 33, 35

Bin 7: 35, 35, 35

Bin 8: 36, 40, 45

Bin 9: 46, 52, 70

Calculate mean for each bin and replace each value with this mean:

Bin 1 mean: (13+15+16)/3 = 15; replaced with 15,15,15

Bin 2 mean: (16+19+20)/3 = 18; replaced with 18,18,18

Bin 3 mean: (20+21+22)/3 = 21; replaced with 21,21,21

Bin 4 mean: (22+25+25)/3 = 24; replaced with 24,24,24

Bin 5 mean: (25+25+30)/3 = 27; replaced with 27,27,27

Bin 6 mean: (33+33+35)/3 = 34; replaced with 34,34,34

Bin 7 mean: (35+35+35)/3 = 35; replaced with 35,35,35

Bin 8 mean: (36+40+45)/3 = 40; replaced with 40,40,40

Bin 9 mean: (46+52+70)/3 = 56; replaced with 56,56,56

This method reduces noise in the data, helping produce more reliable results.

b) Outlier identification:

Outliers are values significantly different from the rest. One may detect them using box-and-whisker plots (box plots) or by calculating the interquartile range.

c) Other smoothing techniques include:

- Binning by boundaries

- Exponential smoothing

- Random walk smoothing

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Response:

1 B

2 A

3 B

Detailed explanation:

1

The population refers to the entire sample from which part of the event is being analyzed. Essentially, in a set, the population includes everything collectively. From the provided statement, our goal is to identify the population. The population is B.

All NBA players since 1966. This selection is because it is from this set that the draft picks were chosen, ultimately narrowed down to 45% being center backs.

2

The specified attribute is A.

Being a No. 1 draft pick, as it's the central focus of the statement itself

3

B sample proportion. As mentioned earlier, the population consists of all NBA players since 1966, so a population proportion would contain a statement like this.

45% of all NBA players since 1966...

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18 days ago
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?
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Answer:

The transformation is a reflection over the x-axis followed by a translation 6 units left and 2 units down.

Step-by-step explanation:

To determine the order of transformations from ΔABC to ΔA"B"C", note that the figure first changes to ΔA'B'C', and then to ΔA''B''C''.

The transition from ΔABC to ΔA'B'C' involves a reflection over the x-axis, as ΔA'B'C' appears as a mirror image flipped vertically.

Next, moving from ΔA'B'C' to ΔA''B''C'' entails shifting the figure left by 6 units and downward by 2 units. This matches a translation by -6 in the x direction and -2 in the y direction.

Thus, the accurate description is:

Reflection across the x-axis followed by a translation of -6 units in x and -2 units in y.

4 0
1 month ago
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Four hot air balloons each descend 295 feet per minute for 7 minutes. Find the total change in altitude for all 4 balloon
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Answer: A total descent of 8260 feet occurred for all four balloons.

Step-by-step explanation:

Based on the information provided:

Number of hot air balloons = 4

Minutes of descent = 7

Descent rate per minute = 295 feet

Thus, the overall change in altitude for all four balloons can be calculated as:

295\times 7\times 4\\\\=8260\ feet

Thus, a total descent of 8260 feet was experienced by the four balloons.

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1 month ago
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Let's start by calculating the cost of the first 10 boxes, which totals $75, and the next 10 boxes cost $55.

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Response:

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Detailed breakdown:

This scenario is centered around compound interest, with the formula for compound interest defined as

Provided Data

A = final amount  =?

P = initial principal balance  = $2,500

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