Download Midterm Exam 2 Solutions - Basic Probability And Statistics | MATH 1105 and more Study notes Mathematical Statistics in PDF only on Docsity!
CHAPTER 1
INTRODUCTION
BACKGROUND
POPULATION RANDOM SAMPLE
Mean (average) =^ ^ Sample mean = X
Proportion = p Sample proportion = p ˆ Mean == Quantitative data (numeric: ratio, interval scales) Proportion == Qualitative data (categorical responses: nominal, ordinal scales) (percentage of voters in favor of a candidate) Statistic: Quantitative measurement calculated on sample data Parameter: Quantitative measurement calculated on population data Statistic is an estimate of the “corresponding” parameter Problem that statistics addresses: Population is so LARGE that resources (money, labor, time) are inadequate to measure every element in the population
Data Scales: Nominal: Values are mere labels (qualitative data) Ordinal: Values are qualitative, but an obvious hierarchy exists for these values Interval: Quantitative data, no real zero, only the distance (interval) between values Is meaningful Ratio: Quantitative, zero -> an absence of the variable
CHAPTER 2
You will have an EXCEL project (not major) to explore graphs and displays that can be created in Microsoft Excel. You can use either Microsoft Excel 2003 or 2007. I will describe the project more in class and will post a document outlining the assignment. We will also have a special class covering EXCEL 2007. Take a look at Chapter 2 examples (EXCEL file) under Course Documents. We will talk about what type of graphs, displays are appropriate for various types of data (qualitative/quantitative, data scales). I will expect you to interpret certain graphs (such as positive, negative correlation)
p 25 Q 1 firstquartile p 75 Q 3 thirdquartile To find the pth^ percentile (as an example), and the sample has n observations, you multiply np (where p is a decimal). This gives you the POSITION where the values of the pth percentile lies (ranking the data from smallest to largest). If np is not an exact integer, increase the result to the next largest integer. You will find the value of the percentile in this position of the ranked data. If np is an exact integer, average the two values in the data at this position and the next position. Example: Here is a sample of 8 observations (already ranked): 3 6 12 16 17 22 29 37 To find the 35th^ percentile, we multiply np = 8 * .35 = 2. Increasing this value to the next largest integer gives 3. We find the 35th^ percentile (p 35 ) as the 3rd^ position. Thus: p 35 = 12. To find the 75th^ percentile, we multiply n*p = 8 * .75 = 6. This is an exact integer. So, the rule is: average the two values in the data set at positions 6 and 7. So: p 75 = (22 + 29) / 2 = 25.
2) Variability: spread in the data
a) Variance: ( 1 ) 2 (^ )^2
n X X s b) Standard deviation: s s^2 Variance (standard deviation must be non-negative) c) Interquartile range (IQR) = Q 3^ ^ Q 1 (insensitive to outliers)
Outlier Detection:
Symmetric Data: Observations more than 3 standard deviations away from the mean are classified as outliers. Skewed Data: Observations more than Q^ 3 ^ (^1.^5 )* IQR or less than Q 1 (^) ( 1. 5 )* IQR are considered to be outliers.
