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4 years ago

find the lower quartile for the data {47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4}

Mathematics

1 answer:

mote1985 [20]4 years ago

3 0

Answer:

The lower quartile is 23.4

Step-by-step explanation:

The given data are;

47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4

Rearranging the data, we have;

5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2

The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term

However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows

5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2

We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile

The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.

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Step-by-step explanation:

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Part a

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$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

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