Survey

Survey

Document related concepts

Transcript

2.3 Measures of Central Tendency (mean, median, mode) Mean (finding the average) β’ Make sure you have these equations written down. β’ π = mu and represents population mean β’ π₯ = sample mean β’ π = population entries β’ π = sample entries Finding a Sample Mean β’ The prices (in dollars) for a sample of round-trip flights from Chicago, Illinois to Cancun, Mexico are listed. What is the mean price of the flights? Finding Median of an odd sample size (middle entry) β’ Find the median of the flight prices (from example 1) below. β’ When finding the median, ALWAYS order the numbers. β’ Median is 427. Finding the Median of an even sample β’ Find the median of the flight prices listed below. β’ Notice they are already organized. β’ Since it is even, find the average of the two middle prices: 397 and 427, which is 412. β’ So the median is 412. Finding the Mode (most frequent) β’ Find the mode of the flight prices from example 1 β’ Organizing the data is not required, but does make it easier. β’ The number that occurs the most frequently is 397. β’ Note: A stem-and-leaf plot would also be helpful when dealing with a large number of entries. Finding the Mode β’ In a survey, 1000 U.S. adults were asked if they thought public cellular phone conversations were rude. Of those surveyed, 510 responded βYes,β 370 responded βNo,β and 120 responded βNot sure.β What is the mode of the responses? Comparing the Mean, Median, and Mode β’ On your own: Find the mean, median and mode of the sample ages of students in a class shown in the table. Which measure of central tendency best describes a typical entry of this data set? Are there any outliers? Start by finding π Ξ£π₯ 475 Mean: π₯ = = = 23.8 years π 21+22 2 20 Median: = 21.5 years Mode: 20 Note: the mean is more affected by outliers than the median. Seeing outliers on a histogram β’ Looking at a histogram for the ages in our sample class, we can see a large gap. In this case, the median would be the best measure of central tendency. Finding a weighted mean (π₯ = Ξ£π₯βπ€ , Ξ£π€ π€ = weight) It will help to organize the data into a table of some sort. Finding a weighted mean cont. Plugging it into the formula: π₯ = Ξ£π₯βπ€ Ξ£π€ = 88.6 1 = 88.6 Finding a weighted mean cont. β’ For the month of May, a checking account has a balance of $523 for 15 days, $1985 for 5 days, $1410 for 5 days, and $348 for 6 days. What is the accountβs mean daily balance for May? Mean of a Frequency Distribution β’ Make sure the equation is written in your notes, be careful it is an approximation. β’ π₯ =the midpoint of a class β’ π = the frequency of the corresponding class β’ π = the total number of frequencies Finding the Mean of a Frequency Distribution β’ Use the frequency distribution at the left to approximate the mean number of minutes that a sample of Internet subscribers spent online during their most recent session. Once again, plugging the information into the 2089.0 formula would be β 41.8 minutes 50 Shapes of distributions Symmetric Uniform Skewed Left Skewed Right Practice Problems β’ Pg. 72 #1 β 4, 9 β 18, 38, 40 β 43