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4 years ago

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Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.20, 22, 25, 28, 2

9, 30, 32, 33, 34
Be sure to show your work for finding:
The lower quartile
The upper quartile
The interquartile range

1 answer:

madreJ [45]4 years ago

7 0

Answer:

The lower quartile is 23.5

The upper quartile is 32.5

The interquartile range is 9

Step-by-step explanation:

The given data set is 20, 22, 25, 28, 29, 30, 32, 33, 34.

The data set is already sorted in ascending order.

The middle number of this data set is called the median.

Therefore the median is 29.

The median divides the data set into two halves.

The lower half is

20, 22, 25, 28

The median of the lower half is the lower quartile.

$Q_1 = \frac{22 + 25}{2} = \frac{47}{2} = 23.5$

The upper half is 30, 32, 33, 34

The median of the upper half is the upper quartile.

$Q_3= \frac{33 + 32}{2} = 32.5$

The interquartile range is given by

$IQR=Q_3-Q_1 \\ IQR=32.5 - 23.5 = 9$

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One number is one more than another. Their sum is nine. Find both numbers.

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Answer:

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Step-by-step explanation:

Let's make an equation to solve. Let's call "one number" x. Another number is 1 more than x, so now we have x + 1. x plus x + 1 is equal to 9... and this gives us our equation:

x + (x + 1) = 9

We can now simplify by adding like terms together:

2x + 1 = 9

Now, let's take away 1 from both sides:

2x = 8

We can finally divide both sides by 2 to isolate x:

x = 4

One of our numbers is 4. Our other number is one more than 4, and 4 + 1 = 5. So our numbers are 4 and 5.

Hopefully this was helpful! If you need more help, let me know.

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3 years ago

What is the perimeter of a square whose diagonal is 13.010

miskamm [114]

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Hope this helps!!!!

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4 years ago

Solve the following compound inequality: (1 point)

valentinak56 [21]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4$

____________________________________

$\large \tt Solution \: :$

$\textsf{First Inequality :}$

$\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4$

$\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4$

$\qquad \tt \rightarrow \: - 2x - 10 > x - 4$

$\qquad \tt \rightarrow \: - 10 + 4 > x + 2x$

$\qquad \tt \rightarrow \: - 6 > 3x$

$\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x$

$\qquad \tt \rightarrow \: - 2 > x$

$\qquad \tt \rightarrow \: \therefore x < - 2$

$\textsf{Second Inequality :}$

$\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)$

$\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24$

$\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x$

$\qquad \tt \rightarrow \: 36 < 9x$

$\qquad \tt \rightarrow \: \cfrac{36}{9} < x$

$\qquad \tt \rightarrow \: 4 < x$

$\qquad \tt \rightarrow \: \therefore x > 4$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

7 0

2 years ago