# Find the mean and median wage. A supervisor at $1,200 a week, an inventory manager at$700 a week, six stock boys at $400 a week and four drivers at$500 are employed by a small warehouse. Mean: The sum of all the entries divided by the total number of entries is known mean. Question
Summarizing quantitative data Find the mean and median wage.
A supervisor at $$\1,200$$ a week, an inventory manager at $$\700$$ a week, six stock boys at $$\400$$ a week and four drivers at $$\500$$ are employed by a small warehouse.
Mean:
The sum of all the entries divided by the total number of entries is known mean. 2021-02-11
Calculation:
The formula for mean is,
$$\overline{x}=\frac{\sum x}{n}$$
Substitute the values and nas 4 in the formula,
$$\overline{x}=\frac{1,200+700+6(400)+4(500)}{12}$$
$$\frac{6,300}{12} = 525$$
Thus, the mean wage is $$\525$$.
Median:
- If the data set consists of odd number of entries then the median is the middle value of the data.
- If the data set consists of even number of entries then the median is the mean of the middle vales in the data set.
Arrange the data in ascending order.
400, 400, 400, 400, 400, 400, 500, 500, 500, 500 700, 1,200
Here the number of observations is 12 which is an even number. Therefore the median is the average of the middle values of the data that is, $$6^{th}\ and\ 7^{th}$$,
The $$6^{th}$$ observation represents 400 and $$7^{th}$$ observation represents 500. Therefore the median is, $$Median = \frac{400+500}{2}$$
$$= \frac{900}{2}= 450$$
Thus, the median wage is $$\450$$.

### Relevant Questions Explain which measure of center best describes a typical wage at this company:the mean or the median. Find the number of employees earn that are more than mean wage. The manager at Publix recently received information that customer satisfaction dropped at noon due to overcrowding in the checkout aisle. As a result, the manager went to the main floor to record the number of customers waiting in aisles 1-10 at noon.
Which of the following choices would be an accurate description of the way the "number of customers" is used in this data set?
a. individuals for the data set
b. continuous qualitative variable for this data set
c. discrete qualitative variable for this data set
d. qualitative variable for this set
e. continuous quantitative variable for this data set
f. discrete quantitative variable for this data set 1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{G}{e}{n}{d}{e}{r}\backslash{h}{l}\in{e}{A}{f}{f}{i}{l}{a}{t}{i}{o}{n}&{M}{a}\le&{F}{e}{m}{a}\le\backslash{h}{l}\in{e}{D}{e}{m}{o}{c}{r}{a}{t}&{300}&{600}\backslash{R}{e}{p}{u}{b}{l}{i}{c}{a}{n}&{500}&{300}\backslash{O}{t}{h}{e}{r}&{200}&{100}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{i}{z}{e}\ {o}{f}\ {C}{a}{r}\backslash{h}{l}\in{e}{G}{e}{n}{d}{e}{r}&{S}{m}{a}{l}{l}&{M}{e}{d}{i}{u}{m}&{l}{a}{n}\ge&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{F}{e}{m}{a}\le&{58}&{63}&{17}&{138}\backslash{M}{a}\le&{79}&{61}&{25}&{165}\backslash{T}{o}{t}{a}{l}&{137}&{124}&{42}&{303}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ? True or false: The mean, median, and mode can all be used with quantitative data. Explain your answer 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 small drugstore orders copies of a certain magazine for it magazine rack each week. Let X=demand for the magazine, with pmf
$$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{1}&{2}&{3}&{4}&{5}&{6}\backslash{h}{l}\in{e}{p}{\left({x}\right)}&{\frac{{{1}}}{{{15}}}}&{\frac{{{2}}}{{{15}}}}&{\frac{{{3}}}{{{15}}}}&{\frac{{{4}}}{{{15}}}}&{\frac{{{5}}}{{{15}}}}&{\frac{{{6}}}{{{15}}}}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
Suppose the store owner actually pays $1.00 for each copy of the magazine and the price to customers is$2.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? Several models have been proposed to explain the diversification of life during geological periods. According to Benton (1997), The diversification of marine families in the past 600 million years (Myr) appears to have followed two or three logistic curves, with equilibrium levels that lasted for up to 200 Myr. In contrast, continental organisms clearly show an exponential pattern of diversification, and although it is not clear whether the empirical diversification patterns are real or are artifacts of a poor fossil record, the latter explanation seems unlikely. In this problem, we will investigate three models fordiversification. They are analogous to models for populationgrowth, however, the quantities involved have a differentinterpretation. We denote by N(t) the diversification function,which counts the number of taxa as a function of time, and by rthe intrinsic rate of diversification.
(a) (Exponential Model) This model is described by $$\displaystyle{\frac{{{d}{N}}}{{{\left.{d}{t}\right.}}}}={r}_{{{e}}}{N}\ {\left({8.86}\right)}.$$ Solve (8.86) with the initial condition N(0) at time 0, and show that $$\displaystyle{r}_{{{e}}}$$ can be estimated from $$\displaystyle{r}_{{{e}}}={\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{N}{\left({t}\right)}}}{{{N}{\left({0}\right)}}}}\right]}\ {\left({8.87}\right)}$$
(b) (Logistic Growth) This model is described by $$\displaystyle{\frac{{{d}{N}}}{{{\left.{d}{t}\right.}}}}={r}_{{{l}}}{N}\ {\left({1}\ -\ {\frac{{{N}}}{{{K}}}}\right)}\ {\left({8.88}\right)}$$ where K is the equilibrium value. Solve (8.88) with the initial condition N(0) at time 0, and show that $$\displaystyle{r}_{{{l}}}$$ can be estimated from $$\displaystyle{r}_{{{l}}}={\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{K}\ -\ {N}{\left({0}\right)}}}{{{N}{\left({0}\right)}}}}\right]}\ +\ {\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{N}{\left({t}\right)}}}{{{K}\ -\ {N}{\left({t}\right)}}}}\right]}\ {\left({8.89}\right)}$$ for $$\displaystyle{N}{\left({t}\right)}\ {<}\ {K}.$$
(c) Assume that $$\displaystyle{N}{\left({0}\right)}={1}$$ and $$\displaystyle{N}{\left({10}\right)}={1000}.$$ Estimate $$\displaystyle{r}_{{{e}}}$$ and $$\displaystyle{r}_{{{l}}}$$ for both $$\displaystyle{K}={1001}$$ and $$\displaystyle{K}={10000}.$$
(d) Use your answer in (c) to explain the following quote from Stanley (1979): There must be a general tendency for calculated values of $$\displaystyle{\left[{r}\right]}$$ to represent underestimates of exponential rates,because some radiation will have followed distinctly sigmoid paths during the interval evaluated.
(e) Explain why the exponential model is a good approximation to the logistic model when $$\displaystyle\frac{{N}}{{K}}$$ is small compared with 1.  