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Recent questions in High school statistics

ttyme411gl 2022-07-07

Boxplot: whiskers and outliers doubt
I have a doubt on boxplot.
I'll expose my knowledge and then my doubt.
$x = {x_{1}, x_{2} . . . x_{n}}$ : the set of samples
$q_{1}$ , $q_{3}$ : the first and third quartiles
$w_{l}$ , $w_{u}$ : the lower and upper whiskers
$I Q R = q_{3} - q_{1}$
box extends from $q_{1}$ to $q_{3}$
$w_{l} = m a x (m i n (x), q_{1} - 1.5 \cdot I Q R)$
$w_{u} = m i n (m a x (x), q_{3} + 1.5 \cdot I Q R)$
$o u t l i e r s = {x_{i} \in x | x_{i} < w_{l} \lor x_{i} > w_{u}}$
Observations:
$whiskers' distance from box are not symmetric ⟺ (w_{l} = m i n (x) \lor w_{u} = m a x (x))$
$w_{u} - q_{3} < q_{1} - w_{l} ⟹ ∄ x_{i} : x_{i} \in o u t l i e r s \land x_{i} > w_{u}$
$w_{u} - q_{3} > q_{1} - w_{l} ⟹ ∄ x_{i} : x_{i} \in o u t l i e r s \land x_{i} < w_{l}$
My doubt: if all what I exposed is correct, how do you explain the presence of outliers in this speed of light boxplot (third experiment, lower outliers) and in this plot (see wednesday, lower outliers)?
In the case my reasoning is wrong, please provide a simple numeric counterexample.

Shea Stuart 2022-07-05

Why is the y intercept for this equation positive?
Rational function
$\frac{(x + 1) (3 x + 2)}{{(x + 1)}^{2}}$
I have found that the two asymptotes are: $y = 3$ and $x = - 1$ and there are no turning points for this function.
To find the $x$ intercept:
$0 = \frac{(x + 1) (3 x + 2)}{{(x + 1)}^{2}}$
Hence
$3 x^{2} - x - 2 = 0$
$x_{1} = 1 x_{2} = - \frac{2}{3}$
Simularly to find the $y$ intercept I did the following:
$\frac{(0 + 1) (3 (0) + 2)}{{(0 + 1)}^{2}}$
$y = - 2$
However plotting this into a graphing software shows that the $y$ intercept is $y = 2$ and $x$ intercept is only $x = - \frac{2}{3}$ and not $x = 1$ .
Why are the intercepts incorrect?

woowheedr 2022-07-03

In $y = 5 x + 6$ , is the $6$ the $y$ -intercept or the $x$ -intercept?

Frederick Kramer 2022-07-03

I know how to find the parabola quadratic equation given the roots. However, in this problem I'm given the y-intercept of (0,3) {So, now I know C value} and the axis of symmetry of x=-3/8. From this I know that 3a=4b. But, it seems I need one more point, since I have 3 unknowns, I'd need 3 INDEPENDENT equations.
So, I said, ah, I know another point, it's on the other side of the aos. So, I used (-3/4, 3). However, when I plug this in, it appears to not be an independent equation. So, I'm left with just c=3 and 3a=4b. How, do I work this from here?

2nalfq8 2022-07-01

How to prove that $\frac{x}{a} + \frac{y}{b} = 1$ where $a$ is the $x$ -intercept and $b$ is the $y$ -intercept for all $a, b \neq 0$

Emanuel Keith 2022-06-27

Which of the following is the $y$ −intercept of a parabola represented by the equation $y = (x^{2}) - 3 x - 4$ ?
$0$
$1$
$- 4$
$- 6$

Mara Cook 2022-06-27

Function: $f (x) = \frac{\sin (x)}{x}$ . Why is the $y$ -intercept $= 1$ despite $\sin (0)$ being divided by zero?

Jackson Duncan 2022-06-26

How to count $n$ th percentile from normally distributed random variable?
I have normally distributed random variable $X \sim N (100, 225)$ . How to count $n$ th percentile?
In my case I need lower quartile - $x (0.25)$

Emmy Knox 2022-06-26

Two parallel lines, the equation of the first line is
$y = - x - 3.$
The distance between the parallel lines is $0.5$ . How do I find the $y$ -intercept of the second line?

dourtuntellorvl 2022-06-26

What is the slope of a line that has an X-Intercept of 8 and a Y-Intercept of 11?

Lucille Cummings 2022-06-26

Is the lower quartile here $18.5$ or $27$ ?
Take the following list of data:
$4 10 27 27 29 34 34 34 37$
If I remove the median which is $29$ then the left hand side is:
$4 10 27 27$
The median of this side is $\frac{10 + 27}{2} = 18.5$
But if I use the percentile formula:
$P_{25} = \frac{25}{100} 9 = 2.25$
$2.25$ is not a whole number so we take the next whole number which is $3$
The $P_{25}$ is the third value which is $27$
Note: Wikipedia defines the lower quartile as the middle number between the lowest number and the median. In this case it would be $27$
Which of these is the lower quartile, $18.5$ , $27$ , or somethings else?

pachaquis3s 2022-06-25

How do I calculate the quartiles for this problem?
I have the following list of numbers, and I'm trying to calculate the quartiles:
2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9
I'm running into a bit of confusion because the median turns out to be 7. Now I don't know how to demarcate the lower group from the upper group since there are a whole bunch of 7's. Consequently, I don't know how to calculate $Q_{1}$ and $Q_{3}$

jermonika13 2022-06-24

Consider all three-digit numbers that can be created from the digits 0-9 $0 - 9$ where the first and last digits must be odd and no digit can repeat. What is the probability of choosing a random number that starts with 7 $7$ from this group? Enter a fraction or round your answer to 4 $4$ decimal places, if necessary.

Hailie Blevins 2022-06-24

Let $f (x) = \frac{x^{2} + 1}{x^{2} - 9}$
So to find the y intercept I take $f (0)$ correct? So when I substitute $0$ for $x$ I got $- \frac{1}{9}$ so is the $y$ intercept $(0, - \frac{1}{9})$
Also to find the $x$ intercept I set the numerator equal to $0$ . So then I got $x^{2} + 1 = 0$ but wouldn't that make $x^{2} = - 1$ which is imaginary?

gvaldytist 2022-06-23

Need help with the steps of finding the slope and $y$ -intercept of this equation: $f (x) = 3 x - \frac{1}{5}$

Amber Quinn 2022-06-22

Suppose a line goes through the points $A = (x_{1}, y_{1})$ and $B = (x_{2}, y_{2})$ . One can easily check (as I did today while doodling) that
$b = - \frac{x_{1} y_{2} - x_{2} y_{1}}{x_{2} - x_{1}}$
where $b$ is the y-coordinate of the $y$ -intercept. This can be written more suggestively as
$\begin{matrix} (1) & b = - \frac{det (A, B)}{Δ x} \end{matrix}$
The presence of det(A,B) suggests a geometrical interpretation, but I couldn't think of one. This reminds me of Cramer's Rule, but I couldn't make that connection explicit either.

Emmy Knox 2022-06-21

How to calculate lower & upper quartiles?
I'm sure this has been asked many times before but it's confusing me a lot so hopefully someone can help!
I am given this data set:
$\begin{array}{r} 0.28 & 0.30 & 0.42 & 0.59 & 0.71 & 1.67 \\ 1.82 & 2.39 & 4.71 & 4.79 & 4.89 & 5.00 \\ 5.00 & 5.76 & 6.09 & 6.17 & 6.81 & 7.12 \\ 7.44 & 8.05 & 8.59 & 8.86 & 9.04 & 9.78 \end{array}$
There are $24$ numbers here. I need to find the lower & upper quartile. I figured that the median is $5.00$
And looking at the answer sheet the Lower Quartile is $1.745$ and the Upper quartile is $7.28$
My question is how do i get to these answers!?
Thank you in advance.

Poftethef9t 2022-06-21

The graph of the quadratic function $y = (x - h)^{2} + k$ passes through $(3, 7)$ and $(4, 11)$ . The axis of symmetry is the graph is $x = 2$ . How can I find the $y$ -intercept of the graph? I know that it is the value of $k$ (the minimum value of the function) but how could I find it?

Spencer Marvin P. Esguerra2022-06-20

C. Find the length of the confidence interval given the following data:(s – sample
standard deviation)
1. 𝑠 = 2.36, n = 350, confidence level: 99%
2. 𝑠 = 3.35, n = 250, confidence level: 99%
3. 𝑠 = 3, n = 275, confidence level: 95%
4. 𝑠 = 6, n = 425, confidence level: 98%
5. 𝑠 = 9, n = 501, confidence level: 99%

audui262 2022-06-19

0<y<1,y<x+1,x<0

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