Useful Examples of Descriptive Statistics

George Bray 2022-06-24

What is the formula to convert a z-score to its appropriate percentile? I assume there is a formula.

freakygirl838w 2022-06-24

A formula to calculate the mode for grouped data's is given:
Mode = $l + \frac{(f_{1} - f_{0}) h}{2 f_{1} - f_{0} - f_{2}}$
Where, $l =$ lower limit of the modal class,
$h =$ size of the class interval,
$f_{1} =$ frequency of the modal class,
$f_{0} =$ frequency of the class preceding the modal class,
$f_{2} =$ frequency of the class succeeding the modal class.
Explain the derivation of this formula.

Dale Tate 2022-06-24

What is a random variable? What is an example of a discrete random variable and a continuous random variable?

abbracciopj 2022-06-24

How do you know which variable is the "x" and the "y"?

Sonia Gay 2022-06-21

How many independent variables can an experiment have?

flightwingsd2 2022-06-21

The distribution is left-skewed if meanThe distribution is right-skewed if mean>median>mode.
Can mode lie between mean and median?

rose2904ks 2022-06-21

Given is a lognormal distribution with median $e$ and mode $\sqrt{e}$ . What is the variance of the lognormal distribution?
Not sure how to solve this. A variable $Y$ has a lognormal distribution if $\log (Y)$ has a normal distribution. So I'm thinking you can solve the question by finding the mean and standard deviation of the associated normal distribution by using the given median and mode. But I don't know how to. For a normal distribution, the median and mode equal the mean, but for a lognormal distribution they evidently do not. How to use these values to find the variance?

preityk7t 2022-06-21

Is temperature a discrete or continuous variable?

Yesenia Sherman 2022-06-21

What books are there that cover elementary algebra, but are not bloated with pedagogically padding?. I searched in this website and the web in general, but the books I could find about elementary algebra are full of pedagogical padding (lots of meta, repetitive examples, fancy formatting, little-relevance images and so on, as if they were written for kids); I find that distracting, and it makes harder to locate material as the density is much lower than in a book like Serge Lang's Algebra or Rudin's Prinicples of Mathematical Analysis.
Could you please recommend a book that covers (even if it is not its main topic) elementary algebra, but from an approach closer to that found in undergraduate-level books (including proofs and excluding pedagogical padding)?.
I know most of what is included in an elementary algebra course, but I want to review this area to make sure I will not miss something elementary when studying more advanced mathematics. I mainly want to review the manipulations of real and complex expressions, rather than things like what a function or a linear equation is.

arridsd9 2022-06-21

Can anyone explain when should I add 0.5 to the z-score?

George Bray 2022-06-21

need to generate some random data from lognormal distribution, where I set the mode and standart deviation of that lognormal distribution. For this purpose I choose to use random numbers generator from lognormal distribution. This generator takes two numbers, that are mean and sd of underlying normal distribution.
So far its clear I need to derive mean and sd of normal distribution, which is underlaying for lognormal distribution where I know mode and sd. I know the equations for derivation of mean and sd:
NOTATION:
$n (x) =$ mean of normal distribution
$s d (x) = s d$ of normal distribution
$n (y) =$ mean of lognormal distribution
$s d (y) =$ sd of lognormal distribution
$m o d e (y) =$ mode of lognormal distribution
EQUATIONS:
$n (x) = 2 * l n (n (y)) - (1 / 2) * l n (s d (y)^{2} + n (y)^{2})$
$s d (x) = - 2 * l n (n (y)) + l n (s d (y)^{2} + n (y)^{2})$
$m o d e (y) = e x p (n (y) - s d (y)^{2})$
Here I stuck because I cant get the equation for $n (y)$ from these equations, that I need to compute $n (x)$ . So far I ended:
$m o d e (y) = e x p (4 * l n (n (y)) - 3 / 2 * l n (n (y)^{2} - s d (y)^{2}))$
$m o d e (y)^{2 / 3} * s d (y)^{2} = n (y)^{2} * (n (y)^{2 / 3} - m o d e (y)^{2 / 3})$
Can anybody help me to complete this derivation?

Sarai Davenport 2022-06-20

How mean i.e. average be equal to mode? What I understand is that median will be the point that is equidistant from the two extremes so here the peak in the bell curve will be the median.
Mode is the item that has occurred frequently - so the peak point has occurred twice - also , the extremes has occurred twice. but I take pairs (x, y)then probably I can say that the peak is the mode.
What I can't understand is the average? How the average will be the highest point. Basically, If I just consider three points - two extreme and the highest then the average will not be the highest point. So, I couldn't understand that the bell curve has the median, mode and mean equal.

gledanju0 2022-06-20

Used the ECB mode (with block length $4$ ) to encrypt the message $m = 1011000101001010$ into $c = 0010011001001101$ using the key
$π = (\begin{matrix} 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \end{matrix})$
and initialisation vector $I V = 1010$ . Now I to decrypt it we used the key
$π^{- 1} = (\begin{matrix} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \end{matrix})$
however isn't the inverse of a permutation it written backwards? In this case shouldn't we have
$π^{- 1} = (\begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 4 & 3 & 2 \end{matrix})$
Why is it the first one?

Leah Vasquez2022-06-19

Find the expected count and the contribution to the chi-square statistic for the (Group 1, No) cell in the two-way table below.

Yes No Total
Group 1 56 44 100
Group 2 135 65 200
Group 3 67 26 93
Total 258 135 393

Round your answer for the expected count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Find the expected count and the contribution to the chi-square statistic for the (C,D)
cell in the two-way table below.

D E F G Total
A 37 33 39 37 146
B 74 93 68 59 294
C 17 35 29 32 113
Total 128 161 136 128 553

Round your answer for the expected count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Find the expected count and the contribution to the chi-square statistic for the (Treatment, Strongly Disagree) cell in the two-way table below.

Strongly Agree Agree Neutral Disagree Strongly Disagree
Control 39 47 5 15 11
Treatment 60 46 11 3 1

Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Find the expected count and the contribution to the chi-square statistic for the (Group 1, No) cell in the two-way table below.

Yes No
Group 1 739 262
Group 2 1155 319

Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Give the degrees of freedom for the chi-square test based on the two-way table.

Yes No Total
Group 1 56 44 100
Group 2 132 68 200
Group 3 72 28 100
Total 260 140 400

Consider the data with analysis shown in the following computer output:

Level N Mean StDev
A 6 10.100 2.882
B 5 16.800 2.168
C 4 10.800 2.387

Source DF SS MS F P
Groups 2 138.60 69.30 10.74 0.002
Error 12 77.42 6.45
Total 14 216.02

What is the pooled standard deviation? What degrees of freedom are used in doing inferences for these means and differences in means?

Round your answer for the pooled standard deviation to two decimal places.

Consider the data with analysis shown in the following computer output:

Level N Mean StDev
A 5 86.950 5.002
B 5 76.167 6.555
C 7 80.000 9.230
D 7 69.333 6.154

Source DF SS MS F P
Groups 3 973.93 324.64 6.43 0.003
Error 20 1010.34 50.52
Total 23 1984.27

What is the pooled standard deviation? What degrees of freedom are used in doing inferences for these means and differences in means?

Round your answer for the pooled standard deviation to two decimal places

Use the following ANOVA table for regression to answer the questions.

Analysis of Variance

Source DF SS MS F P
Regression 1 286.6 286.6 1.85 0.176
Residual Error 174 26952.6 154.9
Total 175 27239.2

Give the F-statistic and p-value.

Enter the exact answers.

Use the following ANOVA table for regression to answer the questions.

Analysis of Variance

Source DF SS MS F P
Regression 1 3401.4 3401.4 19.6 0.000
Residual Error 174 30189.0 173.5
Total 175 33590.4

Give the F-statistic and p-value.

Use the following ANOVA table for regression to answer the questions.

Response: Y

Source DF Sum Sq Mean Sq F-value Pr(>F)
Regression 1 347.95 347.95 13.27 0.000
Residual Error 359 9412.98 26.22
Total 360 9760.93

Give the F-statistic and p-value.

Use the following ANOVA table for regression to answer the questions.

Response: Y

Source DF Sum Sq Mean Sq F-value Pr(>F)
Regression 1 10.756 10.756 2.89 0.090
Residual Error 342 1272.924 3.722
Total 343 1283.680

Give the F-statistic and p-value.

Enter the exact answers.

Two intervals are given, A and B, for the same value of the explanatory variable.
A: 99 to 115 ; B: 92 to 122 ;

(a) Which interval is the confidence interval for the mean response?

Choose the answer from the menu in accordance to item (a) of the question statement

Which interval is the prediction interval for the response?

Choose the answer from the menu in accordance to item (a) of the question statement

(b) What is the predicted value of the response variable for this value of the explanatory variable?

Enter the exact answer.

Two intervals are given, A and B, for the same value of the explanatory variable.
A: 10 to 12 ; B: 4 to 18 ;

(a) Which interval is the confidence interval for the mean response?

Choose the answer from the menu in accordance to item (a) of the question statement

Which interval is the prediction interval for the response?

Choose the answer from the menu in accordance to item (a) of the question statement

(b) What is the predicted value of the response variable for this value of the explanatory variable?

Enter the exact answer.

Two intervals are given, A and B, for the same value of the explanatory variable.
A: 3.9 to 7.5 ; B: 4.4 to 7.0 ;

(a) Which interval is the confidence interval for the mean response?

Choose the answer from the menu in accordance to item (a) of the question statement

Which interval is the prediction interval for the response?

Choose the answer from the menu in accordance to item (a) of the question statement

(b) What is the predicted value of the response variable for this value of the explanatory variable?

Enter the exact answer.

Two intervals are given, A and B, for the same value of the explanatory variable.
A: 15.8 to 23.2 ; B: 15.4 to 23.6 ;

(a) Which interval is the confidence interval for the mean response?

Choose the answer from the menu in accordance to item (a) of the question statement

Which interval is the prediction interval for the response?

Choose the answer from the menu in accordance to item (a) of the question statement

(b) What is the predicted value of the response variable for this value of the explanatory variable?

Enter the exact answer.

	Yes	No	Total
Group 1	56	44	100
Group 2	135	65	200
Group 3	67	26	93
Total	258	135	393

	D	E	F	G	Total
A	37	33	39	37	146
B	74	93	68	59	294
C	17	35	29	32	113
Total	128	161	136	128	553

	Strongly Agree	Agree	Neutral	Disagree	Strongly Disagree
Control	39	47	5	15	11
Treatment	60	46	11	3	1

	Yes	No
Group 1	739	262
Group 2	1155	319

	Yes	No	Total
Group 1	56	44	100
Group 2	132	68	200
Group 3	72	28	100
Total	260	140	400

Level	N	Mean	StDev
A	6	10.100	2.882
B	5	16.800	2.168
C	4	10.800	2.387

Source	DF	SS	MS	F	P
Groups	2	138.60	69.30	10.74	0.002
Error	12	77.42	6.45
Total	14	216.02

Level	N	Mean	StDev
A	5	86.950	5.002
B	5	76.167	6.555
C	7	80.000	9.230
D	7	69.333	6.154

Source	DF	SS	MS	F	P
Groups	3	973.93	324.64	6.43	0.003
Error	20	1010.34	50.52
Total	23	1984.27

Source	DF	SS	MS	F	P
Regression	1	286.6	286.6	1.85	0.176
Residual Error	174	26952.6	154.9
Total	175	27239.2

Source	DF	SS	MS	F	P
Regression	1	3401.4	3401.4	19.6	0.000
Residual Error	174	30189.0	173.5
Total	175	33590.4

Source	DF	Sum Sq	Mean Sq	F-value	Pr(>F)
Regression	1	347.95	347.95	13.27	0.000
Residual Error	359	9412.98	26.22
Total	360	9760.93

Source	DF	Sum Sq	Mean Sq	F-value	Pr(>F)
Regression	1	10.756	10.756	2.89	0.090
Residual Error	342	1272.924	3.722
Total	343	1283.680

Armeninilu 2022-06-19

Gloria is designing an experiment to investigate how different kinds of wheels accelerate down a ramp. Which is the dependent variable?

Abram Boyd 2022-06-19

What are the coefficients in the expression $6 p^{2} + 4 p$ ?

Cherry Satingasin2022-06-19

In hypothesis testing, we have scenarios that have both dependent and
independent samples. Give an example of an experiment with (1)
dependent samples and (2) independent samples.

Jeramiah Campos 2022-06-17

What is an independent variable in chemistry?

Amber Quinn 2022-06-17

Suppose
$f_{X} (x) = {\begin{matrix} 0.5 & x = 0 \\ x & 0 < x \leq 1 \end{matrix}$
What is the MODE of this distribution? I think it should be $0$ because it has the highest mass, even though $1$ has the highest density.
Another one
$f_{X} (x) = {\begin{matrix} x & 0 < x \leq 1 \\ 1 & 1 < x \leq 1.5 \end{matrix}$
What would be the MODE in this case? $1 ? 1.5 ?$ or any number in $[1, 1.5]$

Gybrisysmemiau7 2022-06-16

The proportion of people who like playing basketball is 2%, so a student randomly sample 1000, but find the proportion is 4%, if the true proportion is 2%. What the probability that this student detect at least 4% in random sample?
I used the formula, but found the z score is 4.51 which is impossible I think.

Stepwise Descriptive Statistics Learning