Statistics Notes PDF

What is a Statistics? Mention it types. Statistics is the science, or a branch of mathematics that involves collecting, classifying, analyzing, interpreting, and presenting numerical facts and data. Descriptive statistics Inferential statistics Compare Descriptive Statistics and Inferen...

What is a Statistics? Mention it types. Statistics is the science, or a branch of mathematics that involves collecting, classifying, analyzing, interpreting, and presenting numerical facts and data. Descriptive statistics Inferential statistics Compare Descriptive Statistics and Inferential statistics. What are the four Types of Data & Measurement Scales? Nominal Ordinal Interval and Ratio  Nominal: Nominal scales are used for labeling variables, without any quantitative value. “Nominal” scales could simply be called “labels” Employee identification numbers are an example of nominal data. The numbers are used only to differentiate employees and not to make a value statement about them. Examples include gender (male, female), colors (red, blue, green), or types of animals (dog, cat, bird).  Ordinal: ordinal-level measurement can be used to rank or order objects. For example, using ordinal data, a supervisor can evaluate three employees by ranking their productivity with the numbers 1 to 3. The supervisor could identify one employee as the most productive, one as the least productive, and one as somewhere between by using ordinal data. e.g., strongly disagree, disagree, neutral, agree, strongly agree  Interval: Interval scales are numeric scales in which we know both the order and the exact differences between the values. For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.  In interval measurement, you can determine order, equal intervals, and the magnitude of differences between values, but you can't compute ratios.  Ratio: Ratio Level Ratio-level data measurement is the highest level of data measurement. Ratio data have the same properties as interval data, but ratio data have an absolute zero, and the ratio of two numbers is meaningful. This means that zero indicates the complete absence of the attribute being measured.  Examples of ratio data are height, weight, time, volume, and Kelvin temperature. With ratio data, a researcher can state that 180 pounds of weight is twice as much as 90 pounds or, in other words, make a ratio of 180:90. Many of the data gathered by machines in industry are ratio data. Define Measure of Central Tendency. List its types. Measures of central tendency yield information about the center, or middle part, of a group of numbers. mode, the median, the mean, percentiles, and quartiles. Define Mode. Determine the mode for the following numbers. The mode is the most frequently occurring value in a set of data. Define Median.Write the steps to calculate Median. The median is the middle value in an ordered array of numbers. For an array with an odd number of terms, the median is the middle number. For an array with an even number of terms, the median is the average of the two middle numbers. The following steps are used to determine the median. Compute the mean for the following numbers. 12.Define Percentiles. Write the steps to calculate location of Percentiles. Percentiles are measures of central tendency that divide a group of data into 100 parts. There are 99 percentiles because it takes 99 dividers to separate a group of data into 100 parts. The nth percentile is the value such that at least n percent of the data are below that value and at most (100 - n) percent are above that value. 14.Determine the 30th percentile of the following eight numbers: 14, 12, 19, 23, 5,13, 28, 17. 13. What is Quartiles? Quartiles are measures of central tendency that divide a group of data into four subgroups or parts. The three quartiles are denoted as Q1, Q2, and Q3. Determine Q1,Q2,Q3 for 106, 109, 114, 116, 121, 122, 125, 129. 16.Define Interquartile Range. Write its formulae. The interquartile range is the range of values between the first and third quartile. Essentially, it is the range of the middle 50% of the data It is determined by computing the value of Q3 - Q1. 17. Define Mean Absolute Deviation. Write its formulae. 18. Define Variance. Write its formulae. 19.Define Standard Deviation. Write its formulae. 20. Write the formulae for sample Variance and sample Standard Deviation data_vector