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krok68 [10]
3 years ago
9

У

Mathematics
1 answer:
rjkz [21]3 years ago
8 0

Answer:

I think it might be D

Step-by-step explanation:

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3 years ago
Each of 16 students measured the circumference of a tennis ball by four different methods, which were:Method A: Estimate the cir
lys-0071 [83]

Answer:

a) \bar X_A =22.744

\bar X_B =20.7

\bar X_C =21.013

\bar X_D =18.306

b) Median_A =\frac{23+24}{2}=23.5

Median_B =\frac{20.4+20.4}{2}=20.4

Median_C =\frac{21+21}{2}=21

Median_D =\frac{20.7+20.7}{2}=20.7

c) \bar X_A =23.25

\bar X_B =20.7

\bar X_C =21.04

\bar X_D =20.69

Step-by-step explanation:

Data given

Assuming the following data:

Method A: 18.0, 18.0, 18.0, 20.0, 22.0, 22.0, 22.5, 23.0, 24.0,24.0,25.0,25.0, 25.0,25.0,26.0,26.4

Method B: 18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4, 20.4, 20.4,20.5, 21.2. 22.0,22.0, 22.0,22.0,23.6

Method C: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0, 21.0,21.0,21.0, 21.0, 21.5,21.5,21.5,21.5,21.6

Method D: 20.0, 20.0, 20.0,-20.0, 20.2, 20.5, 20.5, 20.7, 20.7,20.7, 21.0, 21.1, 21.5, 21.6, 22.1,22.3.

Part a

The sample mean is defined as:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

If we apply this formula for the four methods we got:

\bar X_A =22.744

\bar X_B =20.7

\bar X_C =21.013

\bar X_D =18.306

Part b

Since the total number of points for each method is 16 and this is an even number we need to calculate the median as the average between the 8th and the 9th position of the data ordered from the smallest to the largest. If we do this we have that:

Median_A =\frac{23+24}{2}=23.5

Median_B =\frac{20.4+20.4}{2}=20.4

Median_C =\frac{21+21}{2}=21

Median_D =\frac{20.7+20.7}{2}=20.7

Part c

The trimmed mean by 20% means that we need to calculate removing the 20% from each of the tails, the 20% of 16 is 3.2, so we need to remove 3 observations from both ends of the data like this:

Method A: 20.0, 22.0, 22.0, 22.5, 23.0, 24.0,24.0,25.0,25.0, 25.0

Method B: 19.6, 20.1, 20.4, 20.4, 20.4, 20.4,20.5, 21.2. 22.0,22.0

Method C: 20.7, 20.8, 20.9, 21.0, 21.0,21.0,21.0, 21.0, 21.5,21.5

Method D: 20.0 20.2, 20.5, 20.5, 20.7, 20.7,20.7, 21.0, 21.1, 21.5.

If we calculate the mean for each method we got:

\bar X_A =23.25

\bar X_B =20.7

\bar X_C =21.04

\bar X_D =20.69

3 0
3 years ago
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