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# Statistics Week 1 01:960:401

Rutgers

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This 3 page Class Notes was uploaded by Chelsea Notetaker on Wednesday August 24, 2016. The Class Notes belongs to 01:960:401 at Rutgers University taught by Michael Miniere in Fall 2016. Since its upload, it has received 73 views. For similar materials see Basic Statistics for Research in Statistics at Rutgers University.

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Date Created: 08/24/16

Statistics 401 Notes Statistics is about collecting data, organizing it, summarization, and then analyzing it. Stats Collecting o Ex: Surveys Organization o Grouping the data using graphs or charts Summarization o Finding the average- median, mean, mode o (center and spread of data- Ex: Standard deviation) o The lesser spread of data (smaller range) = a more reliable source because it is more consistent. Ex: Data with outcomes of 30-70 (40 range) is MORE reliable than a range from 0-100 (100 range) o Population is the set of all units under study Population is represented by a sample of these units (random sample). Analyzing o Based on the sample drawn, you are able to make a conclusion about the population. Variable Numerical (Quantitative) is when the data is measurable or countable o Ex: weight, age, height Discrete: specific pattern that has specific values Continuous: data that varies over an interval (infinite amount of answer between an interval) Categorical (Qualitative) is when the data is NOT measurable o Ex: race or gender Q: How to tell which is numerical or categorical? A: Finding the average must make sense. Ex: Finding the average weight makes sense because you can have an average weight of 100 lbs and that data can be used. Or, finding the average of house numbers will not help. A person can live in house 12 while another lives in house 15 but finding the average of that does not make sense and isn’t useful. However, find the average of how many people LIVE in a house makes sense. Organizing graphs and charts Categorical Data 1. Pie Chart 2. Bar Graph Series 1 Sales 6 1st Qtr 4 2 0 Series 1 2nd Qtr CategoryCategoryCategoryCategory 1 2 3 4 On the exam, the circle must be relatively as round as you can draw it and the bar graph must have categories evenly spread apart. Numerical Data 18, 19, 19, 19, 21, 21, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 26, 26, 26, 28, 28 1. Dot Plot: Make a line graph with values that are in a specific pattern and put an “x” or dot for how many times each number appears. Don’t forget to label axis and give a title for everything. 2. Histogram: Overlapping numbers go to the higher interval. 22 would group with [22-24). Notice the closed bracket. BE SURE TO LABEL AXIS AND TITLE. And there aren’t spaces in between these bars. Age # of people [18-20) 4 8 7 [20-22) 2 6 18-20 5 20-22 [22-24) 4 4 22-24 3 2 24-26 [24-26) 7 1 26-28 [26-28) 5 0 Age Those lines are called tails and if the tails are uneven then it is call skewed. You draw the tails starting at the middle of the tallest bar then draw out following the height of the other bars. Since the tail seems longer towards the left side then it is left skewed. 3. Stem and Leaf Plot Stem Leaf 1 8, 9, 9, 9 2 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 8, 8 Stem is the tens place and leaf is the one’s place. Let’s say there weren’t any number in the 20’s you WOULD NOT write the number 2. If there are number in the 30’s then skip 2 and write 3. If there are decimals just write it in the stem part. Ex: 1.5 [1.] would be in the stem part and [5] would be in the leaf part Or you could write “leaf unit = (however many decimal places)” next to leaf and just write the number normally Ex: .45 Stem | Leaf (leaf unit = .01) because 45 x .01 = .45 --------------- 4 | 50 DON’T FORGET TO SEPARATE BY COMMAS Summarizing Measures of center- to know where the balancing point is which can be found with mean (average), median, mode, or mid-range Mean (average): arithmetic mean. Add all of the numbers then divide by how many numbers there are. (can only be one number) Ex: The quiz scores for a class were 50, 86, 97, 76, and 100. What is the average? (50+86+97+76+100)= 409 then divide by 5 because there are 5 test scores. 409/5 = 81.8 Median: middle value of data that increases, in order, from lowest to highest. (only one number) Mode: The number that appears the most. (can be more than one number) µ = population mean x = sample mean N = # units in pop. n = # units in sample

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