# Calculating appropriate arithmetic mean, median and peak values ​​for equal data group. a) Body weights (kg) of patients who come to a nutrition clinic: 50, 55, 69, 58, 57, 62, 60 b) Height measurements (cm) of children receiving treatment in the pediatric clinic: 120,125, 110, 105, 125, 108, 115, 125, 119 c) Blood urea level (mg / dl): 119, 5, 2, 6, 4, 3, 1 d) In which of the above distributions, arithmetic mean and peak value in hagi are not appropriate center criteria? Why is that?

Question
Modeling data distributions
Calculating appropriate arithmetic mean, median and peak values ​​for equal data group. a) Body weights (kg) of patients who come to a nutrition clinic: 50, 55, 69, 58, 57, 62, 60 b) Height measurements (cm) of children receiving treatment in the pediatric clinic: 120,125, 110, 105, 125, 108, 115, 125, 119 c) Blood urea level (mg / dl): 119, 5, 2, 6, 4, 3, 1 d) In which of the above distributions, arithmetic mean and peak value in hagi are not appropriate center criteria? Why is that?

2020-11-10
Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve. Part a: Body weight: The mean is computed as, $$\displaystyle{M}{e}{a}{n}={\frac{{{50}+{55}+{69}+{58}+{57}+{62}+{60}}}{{{7}}}}$$
$$\displaystyle={\frac{{{411}}}{{{7}}}}$$
$$\displaystyle={58.7143}$$ Thus, the mean is 58.7143. The median is the middle most value when observations are arranged in ascending order. Thus, we have observations in ascending order as 50,55,57,58,60,62,69. Hence, middle most observation is the $$\displaystyle{4}^{{t}}{h}$$ observation. Hence, median = 58. Peak value =maximum value = 69. Part b: Height The mean is computed as, $$\displaystyle{M}{e}{a}{n}={\frac{{{120}+{125}+{110}+{105}+{125}+{108}+{115}+{125}+{119}}}{{{9}}}}$$
$$\displaystyle={\frac{{{1052}}}{{{9}}}}$$
$$\displaystyle={116.8889}$$ Thus, the mean is 116.8889. The median is the middle most value when observations are arranged in ascending order. Thus, we have observations in ascending order as 105,108,110,115,119,120,125,125,125. Hence, middle most observation is the $$\displaystyle{5}^{{t}}{h}$$ observation. Hence, median = 119. Peak value =maximum value = 125 Part c: Blood urea level: The mean is computed as, $$\displaystyle{M}{e}{a}{n}={\frac{{{119}+{5}+{2}+{6}+{4}+{3}+{1}}}{{{7}}}}$$
$$\displaystyle={\frac{{{140}}}{{{7}}}}$$
$$\displaystyle={20}$$ Thus, the mean is 20. The median is the middle most value when observations are arranged in ascending order. Thus, we have observations in ascending order as 1,2,3,4,5,6,119. Hence, middle most observation is the $$\displaystyle{5}^{{t}}{h}$$ observation. Hence, median = 4. Peak value =maximum value = 119.

### Relevant Questions

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
Make a scatterplot for the data.
Height and Weight of Females
Height (in.): 58, 60, 62, 64, 65, 66, 68, 70, 72
Weight (lb): 115, 120, 125, 133, 136, 115, 146, 153, 159
1. The standard error of the estimate is the same at all points along the regression line because we assumed that A. The observed values of y are normally distributed around each estimated value of y-hat. B. The variance of the distributions around each possible value of y-hat is the same. C. All available data were taken into account when the regression line was calculated. D. The regression line minimized the sum of the squared errors. E. None of the above.

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.
The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58 Class Frequency Relative Cumulative Frequency Frequency 10 but less than 20 5 20 but less than 30 4 30 but less than 4 4 40 but less than 50 5 50 but less than 60 2 TOTAL What is the Relative Frequency for the class: 50 but less than 60? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35
The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58 Class Frequency Relative Cumulative Frequency Frequency 10 but less than 20 5 20 but less than 30 4 30 but less than 4 4 40 but less than 50 5 50 but less than 60 2 TOTAL What is the Relative Frequency for the class: 20 but less than 30? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35
The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58 Class Frequency Relative Cumulative Frequency Frequency 10 but less than 20 5 20 but less than 30 4 30 but less than 4 4 40 but less than 50 5 50 but less than 60 2 TOTAL What is the Relative Frequency for the class: 40 but less than 50? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35
1. Find each of the requested values for a population with a mean of $$? = 40$$, and a standard deviation of $$? = 8$$ A. What is the z-score corresponding to $$X = 52?$$ B. What is the X value corresponding to $$z = - 0.50?$$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $$M=42$$ for a sample of $$n = 4$$ scores? E. What is the z-scores corresponding to a sample mean of $$M= 42$$ for a sample of $$n = 6$$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $$\mu = 78$$ and $$\sigma = 12$$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $$82, 74, 62, 68, 79, 94, 90, 81, 80$$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $$12 (\mu = 42, \sigma = 12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is$44.50 from tips. Test for a difference between this value and the population mean at the $$\alpha = 0.05$$ level of significance.
A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.
a) what is the speed at the instant his feet touch theground?
b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?
c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.