Enter 2nd 1 for list L1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O D. The median does not represent the center because it is the least data entry. 0 Choose the correct answer below. Suppose the analyst constructs an R chart to see if the variability in production times is in-control. (Enter your responses rounded to three decimal? So , median = 14th term + 15thterm median = 30+31 = 30.5 And . Choose the correct answer below. Does(Do) the mode(s) represent a typical entry of the data? What is the deseasonalized value at this time point? Choose the correct answer below. \( 53.25(1) + 59.5(0) + 65.5(4 )+ 71.5(4) + 77.5(2) + 83.5(3) + 89.5(4) + 95.5(1) = 1460.25\), \(\mu = \dfrac{\sum{fm}}{\sum{f}} = \dfrac{1460.25}{19} = 76.86\), Data from The World Bank, available online at, Demographics: Obesity adult prevalence rate. Indexmundi. | 0.47 | 0.60 | 0.78 | 0.76 | 0.50 | 0.45 | 0.49 | 0.33 | 0.61 | 0.72 | 0.58 | 0.54 | 0.71 | 0.44, A sample of 11 staff in a company was asked how much money they had in their account banks. What are the measures of central tendency? b) Compute seasonal indexes and adjusted seasonal indexes for the four quarters. QUESTIONA sample of seven admission test scores for a professional school are listed below.11.3 10.9 11.6 10.4 11.2 11.8 10.4Does the median repr. Press 2nd 1 for L1 and then ENTER. Which description below best describes the shape of the distribution. Your IP: (Use a comma to separate answers as needed.) The letter used to represent the sample mean is an \(x\) with a bar over it (pronounced \(x\) bar): \(\overline{x}\). a. O A. Generally, centering makes this value more interpretable, because the expected value of . The majority, about 89 %, of this heat is stored in the ocean, followed by about 6 % on land, 1 % in the atmosphere, and about 4 % available for melting the cryosphere. A statistic is a number calculated from a sample. A data set consists of a set of numerical values. A frequency table is a data representation in which grouped data is displayed along with the corresponding frequencies. Choose the correct answer below. The mean and the median can be calculated to help you find the "center" of a data set. 115 115 14 24 66 42 37 66 85 52. In this particular example, the mean salary is $47,000 while the median salary is $32,000. b. The responses in (thousand dihrams) are 10 15 1 15 28 30 33 32 10 1 40 Determine the following a. Mode, The best fitting line minimizes the vertical distances from the points to the line. In the real world, people make these calculations using software. which is the mean, which is the median, and which is the mode. the data, if possible. |x| y |2| 34.7 |3| 30. This means that: a. there is a seasonal component in the data. Bar graph. Find the midpoint of each interval, multiply by the corresponding number of teenagers, add the results and then divide by the total number of teenagers, \[Mean = (1.75)(3) + (5.5)(7) + (9.5)(12) + (13.5)(7) + (17.5)(9) = 409.75\]. The model is shown below. 54 63 67 50 57 61 62 58 51 A. The midpoint is, \[\dfrac{\text{lower boundary+upper boundary}}{2}.\], We can now modify the mean definition to be, \[\text{Mean of Frequency Table} = \dfrac{\sum{fm}}{\sum{f}}\]. Find the linear regression, For an online auction, the following table presents the prices of a group of items (x) and the number of people participating in the auction (y). Get started with our course today. b. x 77 76 77 72 76 77 y 241 225 241 209 225 227 Compute the correlation coefficient. What is the center line of this R chart? a) Show the four-quarter and centered moving average values for this time series. The data set shown below contains the number of hurricanes that occurred each year over 14 years. Access to over 100 million course-specific study resources, 24/7 help from Expert Tutors on 140+ subjects, Full access to over 1 million Textbook Solutions. Identify the mode of the data set. Y. when . This is discussed in more detail later in the text. places.) Is this home's price ab, Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. To unlock this lesson you must be a Study.com Member. 1 0345 97 b. One of the requirements for the sample mean to be a good estimate of the population mean is for the sample taken to be truly random. Find the mean, median, and mode of the data, if possible. 173.236.168.104 Some other measures of mean used to find the central tendency are as follows: Geometric Mean Harmonic Mean Weighted Mean In a sample of 60 households, one house is worth $2,500,000. One advantage of the __ is that the actual data values are related (kept) in the graphical summarization of the data. The median is 30.5) H The median sekeratriis the center of the data set . The mean represents the center of the data set. a. The mean can be used to get an overall idea or big picture of the data set. Cat has a master's degree in education and is currently working on her Ph.D. Elizabeth is working on a science project. Course Hero is not sponsored or endorsed by any college or university. How to Use the gsub() Function in R (With Examples). This page titled 2.6: Measures of the Center of the Data is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The data are modeled by the equati, The following sample data taken from the "Back of the Bike" ice cream company and contains the temperature (Temp (F)) and the number of boxes of ice cream sold (# of boxes): Compute the regression line to estimate number of ice cream boxes sold. The median does not represent the center because it is the largest data value.Pay someone to do your homework, quizzes, exams, tests, assignments and full class at:https://paysomeonetodo.com/ It is more a coincidence that the mean also is (often, but nor always!) The mean cannot be calculated because there is an even number of data entries. What would be the best measure of the center? Plus, get practice tests, quizzes, and personalized coaching to help you Y. when . A. The durations (in minutes) of power failures at a residence in the last 4 years are listed below. The data below contains the data on the price for two tickets, with online service charges, large popcorn, and two medium soft drinks at a sample of six theater chains: $36.15 $31.00 $35.05 $40.25 $33.75 $43.00 Placed the data into an ordered array. All other trademarks and copyrights are the property of their respective owners. A. Cat has taught a variety of subjects, including communications, mathematics, and technology. Explore the definition of the center in a data set, and review options for finding it, including the mean and median. Heres a quick summary of the main points made in this article: Real Life Examples: Using Mean, Median, & Mode B. It is important to use the correct method for finding the center of data so you can accurately summarize the data set. Consider a weight loss program that advertises a mean weight loss of six pounds the first week of the program. iv) The mode(s) does (do) not represent the center because it (one) is the largest data value. A. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. Cloudflare Ray ID: 7c0aa3e158eb2076 Determine the equation of the linear model. C. The median does not represent the center because it is not a data value. hbbd``b`f+r $X@@bq j ",A\O%Qd@$@b V?KHlFA:Gg4}` jh \[\bar{x} = \dfrac{5,000,000+49(30,000)}{50} = 129,400\], (There are 49 people who earn $30,000 and one person who earns $5,000,000.). I would definitely recommend Study.com to my colleagues. 460 0 obj <> endobj 115 115 14 24 66 42 37 66 85 52 One side has a more spread out and longer tail with fewer scores at one end than the other. An error occurred trying to load this video. Find the mean for the following frequency tables. In the second calculation, the frequencies are 3, 2, 1, and 5. Interpret the slope and the Y-intercept. Your answer is correct . D. The median does not represent the center because it is not a data value. {/eq}. The sample mean \(\bar{x}\) is an example of a statistic which estimates the population mean \(\mu\). Find the mean. The least squares line is Price= 24.93 + 0.094 Capacity (GB) with se = 10.52 and SE(b1) = 0.0030, where the values are rounded, A population data set produced the following information. Half of the rest are worth $280,000, and all the others are worth $315,000. Use the format as an example when submitting your equatio, Data accumulated by the National Climatic Data Center shows that the average wind speed in miles per hour for St. Louis, Missouri is 9.7. Five real estate exam scores are 430, 430, 480, 480, 495. What would be the forecasted attendance with a forecasted temperature of 88 degre. The following data show the number of months patients typically wait on a transplant list before getting surgery. The median does not represent the center because it is not a data entry.c. Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies. The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. endstream endobj 461 0 obj <. The most frequent number of books is 7, which occurs four times. Available online at. 0.778 B. To calculate the mean from a grouped frequency table we can apply the basic definition of mean: \[mean = \dfrac{\text{data sum}}{\text{number of data values}}.\]. The Law of Large Numbers says that if you take samples of larger and larger size from any population, then the mean \(\bar{x}\) of the sample is very likely to get closer and closer to \(\mu\). To do so, they record the number of sales of each server type for each of the last 12 months: Month Int, The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Please include what you were doing when this page came up and the Cloudflare Ray ID found at the bottom of this page. Complete parts (a) and (b). Enrolling in a course lets you earn progress by passing quizzes and exams. Study with Quizlet and memorize flashcards containing terms like A health and fitness club surveys 40 randomly selected members and finds that the average weight of those questioned is 157 lb., After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of the meat was spoiled., From past figures, it is predicted that 39% of the registered voters . Does the median represent the center of the data? That is, exactly half of the values in the dataset are larger than the median and half of the values are lower. (See Sampling and Data for a review of relative frequency). If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilias sample? Find the population regression line. 54 yr, 63 yr, 67 yr, 5. Does the mode represents the center data? A check-processing center uses exponential smoothing to forecast the number of incoming checks each mouth. Create a histogram of the given data. You can email the site owner to let them know you were blocked. A. Y: 32, Provide R code that stores the values 0.90, 0.93, 0.8, 0.95, and 0.91 in a vector named "s"; calculates the number of items stored in "s"; calculates the mean of the values in "s"; calculates the cumulative product of the values in "s"; and plots the valu, Fill in the blank. Computer data: |Year |Sales |1 |69 |2 |159 |3 |258 |4 |389 |5 |546 |6 |890 |7 |2014 |8 |2873. 2 Attachments jpg Find the mode. The median is an important metric to calculate because it gives us an idea of where the center of a dataset is located. N=460, sumx=3920, sumy=2650, sumxy=26,570, sumx2=48,530 Find the population regression line. Ways to Describe Data Distribution | Center, Shape & Spread. The median does not represent the center because it is not a data value. b. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. A computer systems retailer wishes to compare the average monthly sales of its servers with Intel and AMD multi-core processors. A. The median cannot be calculated because the data are at the nominal level of measurement. The data are ordered from smallest to largest. The mean can be used to get an. Each was given the task of estimating the mean distance that shoppers live from the mall. The next example illustrates the location of the median and the value of the median. Choose the correct answer below. The following table shows the average adjusted gross income r, Using the data for Anywhere Health Care Facility, compute the measures of central tendency showing the formula, your work, and the answer. For example, suppose we have a dataset that contains the selling price of 10,000 different homes in a certain city. There is no mode b. Because we have an outlier in this data set, we need to use the median to find the center of the data set. C. The median does not represent the center because it is the smallest data value. Spread Statistics Measures & Examples | What are Spread Statistics? Its like a teacher waved a magic wand and did the work for me. To determine whether the cash bonuses paid by a company are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. b. Choose the correct answer below. c) Determine the least squares trend-line. Learn more about us. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 24; 24; 25; 26; 26; 26; 27; 27; 28; 28; 29; 29; 30; 32; 35; 35; 37; 39; 40. An outlier is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set. Use the following stock price data (in dollars) as input, and write R scripts to calculate the mode of the stock price. Key: 3 | 0 = 30 O B. Instead of staring at rows and rows of raw data, we can calculate the median value to quickly understand the middle selling price of homes in this city. We can see that the median does a better job of capturing the typical square footage of a house on this street compared to the mean because it isnt influenced by the extreme outlier values. From production records, the data in the table below were collected. The durations (in minutes) of power failures at a residence in the last 4 years are listed below. The following data show the measured values for various days. 0 79 It is also known as the arithmetic mean, and it is the most common measure of central tendency. 23689 Which of th, According to inventory records at a shoe store, the number of pairs of sandals (in hundreds) in stock can be approximated by S(x)=9x+175x+5 where x is the number of days since the start of the season. The accompanying data represents the square footage and selling price for the region.Is there a linear relation between square footage and asking price? produced the above tables. How do you know. Over the most recent period (2006-2020), the EEI amounts to 0.760.2 W m 2. See answers Press the down and up arrow keys to scroll. The data show the list and selling prices for several expensive homes. About eight-in-ten U.S. public school teachers (79%) identified as non-Hispanic White during the 2017-18 school year, the most recent year for which NCES has published demographic data about them. Real Life Examples: Using Mean, Median, & Mode The mean is also commonly known as the average. Get unlimited access to over 88,000 lessons. Analysis of the set finds that the regression equation is y = 100 - 3x. hb```5K@(1k3mor,N;25ZAH"r10FiQ 4ABLq``s`YP .f`e@y@.Y2^a_Un * ( Which is the better measure of the center: the mean or the median? A. Find the best estimate of the class mean. # mode is the most repeated values in oun data set number 22 and 33 are the mast repeated number that is 3 times . The median represents the center of the data set BUY Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018 18th Edition ISBN: 9780079039897 Author: Carter N=460, x = 920 , y = 2650 , x y = 26 , 570 , x 2 = 48 , 530. flashcard sets. Find the mean, median, and mode of the data if possible. Does the median represent the center of the data? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Press STAT 1:EDIT. You can email the site owner to let them know you were blocked. Find the intercept of the regression line. Starting at the smallest value, the median is located between the 20th and 21st values (the two 24s): Clear list L1. The mean represents the center. Determine the type of sample that is g. To determine whether the cash bonuses paid by a company are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. E. There is no mean age. Skewed distributions. The median does not represent the center because it is the largest data value. O C. The mean cannot be calculated because the sample size is too small. Equivalent Ratios & Examples | What are Equivalent Ratios? The median is important because it gives us an idea of where the center value is located in a dataset. It helped me pass my exam and the test questions are very similar to the practice quizzes on Study.com. The median tends to be more useful to calculate than the mean when a distribution is skewed and/or has outliers. List price (millions of $) 1.6 4.2 2.1 1.6 2.3 4 Selling price (millions of $) 2 4.6 1.8 1.9 2.4 3.6 A. a) Find the regression e, The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. Station 1: 5030, 13700, 10730, 11400, 860, 2200, 4250, 15040, 4980, 11910, 8130, 26850, 17660, 22800, 1130, 1690 Station 2: 2800, 4670, 6890, 772, Assume that the current date is February 1, 2017 . You can summarize data in different ways by finding the center of data. The mode is the most frequent value. 2 0112225 The median represents the middle value in a dataset. Find the mode of the ages. 2K views, 27 likes, 7 loves, 18 comments, 0 shares, Facebook Watch Videos from Dbstvstlucia: DBS MORNING SHOW & OBITUARIES 25TH APRIL 2023 APRIL 2023 No. If you let the number of samples get very large (say, 300 million or more), the relative frequency table becomes a relative frequency distribution. E. The data set does not have a median. Find the mean, the median, and the mode of a) Find the slope for the trend-line. The following partial computer output summarizes the res, The following another set of data that looking at how long it takes to get to work. The median is O D. The median cannot be calculated because the sample size is too small. A move on a graph is a move from one node to another along a single edge, Determine the coordinates of the points on the logarithmic straight line for 1997 and 2006. a. | 9 E. The data set does not have a mode. The trend value for the second quarter of the year 2005 is 0.75. The accompanying data represents the square footage and selling price for the region. State, The number of laptops per quarter sold by a computer outlet in a suburb was recorded, for three consecutive years from 2011 to 2013. Examples of these measures include the mean, median, and mode. Additional Resources. If \(n\) is an even number, the median is equal to the two middle values added together and divided by two after the data has been ordered. One of the biggest factors in determining the value of a home is the square footage. The median does not represent the center because it is the smallest data value. The mode cannot be calculated because the data are at the nominal level of measurement. - Definition & Options, Calculating the Mean, Median, Mode & Range: Practice Problems, Visual Representations of a Data Set: Shape, Symmetry & Skewness, Unimodal & Bimodal Distributions: Definition & Examples, The Mean vs the Median: Differences & Uses, Spread in Data Sets: Definition & Example, Quartiles & the Interquartile Range: Definition, Formulate & Examples, Finding Percentiles in a Data Set: Formula & Examples, The Effect of Linear Transformations on Measures of Center & Spread, Population & Sample Variance: Definition, Formula & Examples, Ordering & Ranking Data: Process & Example, Study.com SAT Test Prep: Practice & Study Guide, Study.com PSAT Test Prep: Practice & Study Guide, NY Regents Exam - Geometry: Help and Review, McDougal Littell Geometry: Online Textbook Help, Prentice Hall Geometry: Online Textbook Help, GED Math: Quantitative, Arithmetic & Algebraic Problem Solving, Geometry Assignment - Construction & Properties of Triangles, Geometry Assignment - Working with Polygons & Parallel Lines, Geometry Assignment - Calculating the Area of Quadrilaterals, Geometry Assignment - Deriving Equations of Conic Sections, Geometry Assignment - Practicing Analytical Geometry, Geometry Assignment - Probability & Permutations, Geometry Assignment - Using Triangles, Quadrilaterals, Other Polygons & Circles, Geometry Assignment - Geometric Constructions, Conic Sections, Probability & Analytical Geometry, Perpendicular Angles: Definition & Examples, Solving Two-Step Inequalities with Fractions, Solving Systems of Equations Using Matrices, Working Scholars Bringing Tuition-Free College to the Community. Statistical Questions | Statistical vs. Non-Statistical Questions Examples. 0, One of the biggest factors in determining the value of a home is the square footage. The median cannot be calculated because the data are at the nominal level of measurement. Th, The following data represent the concentration of organic carbon (mg/L) collected from organic soil. Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. A company operates four machines during three shifts each day. The median represents the center. A shoe company reports the mode for the shoe sizes of men's sho, A graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). Please include what you were doing when this page came up and the Cloudflare Ray ID found at the bottom of this page. The information in the following table is from the entire section. Create your account. If not, say. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? O B. D. The mean does not represent the center because it is not a data value. It also gives us an idea of the typical value in a given dataset. Try refreshing the page, or contact customer support. Construct a scatterplot, find the value of the linear correlation co, We want to predict the number of coffee shops in a city based on the population of the city. Learn how to find the mean, median, mode and range in a data set, how each is used in math and view examples. The mean does not represent the center because it is not a data entry. The median does not represent the center because it is the smallest data value. OC. A. A. |Speed |Mileage |53 |27 |55 |29 |59 |25 |62|24 |65|26, The data below represents the overall miles per gallon? If the following data (for different types of products) can be represented as a histogram, draw the histogram. 22. We simply need to modify the definition to fit within the restrictions of a frequency table. Statistics exam scores for 20 students are as follows: 50; 53; 59; 59; 63; 63; 72; 72; 72; 72; 72; 76; 78; 81; 83; 84; 84; 84; 90; 93. This number is referred to as the outlier. The $2,500,000 is an outlier. Use the following information to answer the next three exercises: We are interested in the number of years students in a particular elementary statistics class have lived in California. Either $280,000 or $315,000 gives us a better sense of the middle of the data. 10123 3 34 57 A data table shows the number and percent of employees in each of the four categories: daytime employee, daytime manager, nighttime employee, and nighttime manager. Elizabeth is now experimenting with the effectiveness of plain soap on stains. These statistics indicate where most values in a distribution fall and are also referred to as the central location of a distribution. Model Number Price A 8 $10,000 B 10 $12,000 C 12 $8,000, The CEO of a company wishes to interview 15 employees from within his company to analyze worker morale, so he picks 15 random numbers and uses them to select employees from a company directory that lists each worker. The mean is the sum of the numbers in a data set divided by the total number of values in the data set. Select the correct choice below and, if necessary, fill in the answer box to complete. The mean does not represent the center because it is the greatest data entry. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Mean The mean represents the average value of the dataset. They each randomly surveyed 100 shoppers. Median: Starting at the smallest value, the median is the 20th term, which is 13. Does the median represent the center of the data? The action you just performed triggered the security solution. a. This website is using a security service to protect itself from online attacks. Example 1: Calculating the Median of a Skewed Distribution. The mode will tell you the most frequently occuring datum (or data) in your data set. The number of books checked out from the library from 25 students are as follows: 0; 0; 0; 1; 2; 3; 3; 4; 4; 5; 5; 7; 7; 7; 7; 8; 8; 8; 9; 10; 10; 11; 11; 12; 12. Does (Do) the mode (s) represent a typical entry of the data? b. A sm, The sales of a local grocery chain, since 2008 are: Round your answer to 1 decimal place. The following table shows the average petrol price and the number of online shopping orders over a given month: Petrol Price and Online Shopping Average Petrol Price per gallon over a month ($) Number of Online Shopping Orders 4.1525 3,752 2.855 3,289 1. Find and interpret a 95% confidence interval for the gas mileage of 2010 vehicles. The mode(s) is/are The median tends to be more useful to calculate than the mean when a distribution is skewed and/or has outliers. The mode might indicate that most people lose two pounds the first week, making the program less appealing. For example, if the median $ value of the investment 50 thousands, Row 1 will be labeled ?investment under ? A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. I feel like its a lifeline. Stock Price Data: 10 7 20 12 75 15 9 18 4 12 8 14. ii) The mode(s) does (do) not represent the center because it (one) is the smallest data value. The letters A, B, and C are marked on the histogram below. Mean is best used for a data set with numbers that are closer together. (Round to one decimal place as needed.) Multiply each midpoint by the number of values found in the corresponding range. What are some benefits of representing data sets using frequency distributions?, What are some benefits of representing data sets using frequency distributions? The mode is $25,000 and occurs 150 times out of 301. Determine the adjusted seasonal indices. A data set with two modes is called bimodal. Example 2: Calculating the Median When Outliers Are Present. Createyouraccount. Because $25,000 occurs nearly half the time, the mode would be the best measure of the center because the median and mean dont represent what most people make at the factory. The mean does not represent the center because it is the largest data value. The mode is the most frequent value. The mean is the result of a probability model . You can think of a sampling distribution as a relative frequency distribution with a great many samples. Fewer than one-in-ten teachers were either Black (7%), Hispanic (9%) or Asian American (2%). What conclusions can be reached concerning the miles per gallon of mid-sized sedans? mean and median are equal; both located at the center of the distribution; 68 % \approx68\% 6 8 % approximately equals, 68, percent of the data falls within 1 1 1 1 standard deviation of the mean; 95 % \approx95\% 9 5 % approximately equals, 95, percent of the data falls within 2 2 2 2 standard deviations of the mean X) is zero represents the expected value of . Find the mean, median, and mode of the data, if possible. Find the mode(s). Median (With Examples) Choose the correct answer below. C. The median does not represent the center because it is not a data value. B. E. There is no median age. QUESTIONA sample of seven admission test scores for a professional school are listed below.11.3 10.9 11.6 10.4 11.2 11.8 10.4Does the median represent the center of the data?ANSWERA.) Does the mode represents the center data? (MPG) of 2008 SUV's priced under $30,000. Use the method of least squares to compute an estimated regression line betwee, The data below represent the total number of customers in a store and the waiting times at the checkout (in minutes). d. The median cannot be calculated because the sample size is too small. It can be calculated as the sum of all the values in the dataset divided by the number of values. This means the large salaries on the right side of the distribution pull the mean away from the center of the distribution. The median is generally a better measure of the center when there are extreme values or outliers because it is not affected by the precise numerical values of the outliers.
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does the mean represent the center of the data? 2023