NMU_Week 3 Stats.pdf

Statistics (Level 2) zDr.Heba Elsegai Lecturer of Mathematics and Applied Statistics and Insurance Faculty of Commerce – Mansoura University 2024 - 2025  z Terminology § A variable is a characteristic o...

Statistics (Level 2) zDr.Heba Elsegai Lecturer of Mathematics and Applied Statistics and Insurance Faculty of Commerce – Mansoura University 2024 - 2025  z Terminology § A variable is a characteristic or attribute that can assume different values. (Recorded data) § The values that a variable can assume are called data (Raw data – Historical data –Known data). § When organizing data after filtration and pre-processing, we might split data into groups called classes (is also called categories). § Class limits are the lower class limit and the upper class limit, which corresponds to the smallest and the largest number of a class. § Class long is the difference between the lower limit and upper limit of a class. § Class boundary is either lower boundary or upper boundary (It is always +\- 0.5). § Lower class boundary is the lower limit minus 0.5. § Upper class boundary is the lower limit plus 0.5. § Frequency is defined as how many times an element is repeated. Bluman Chapter 1 2  z Important notes Upper limit of a class is not equal to the lower limit of the next class. Upper boundary of a class is equal to the lower boundary of the next class. The class long of any class must be the same or equal for all classes. Bluman Chapter 1 3  z Example of Recorded Values and Boundaries Variable Recorded Value Boundaries Length 15 centimeters 14.5-15.5 cm (cm) Temperature 86° Fahrenheit 85.5-86.5 °F (°F) Time 0.43 second 0.425-0.435 (sec) sec Mass 1.6 grams (g) 1.55-1.65 g  z Levels of Measurement (Type of Scale) § Nominal – categorical (names) § Ordinal – nominal, plus can be ranked (order) § Interval – ordinal, plus intervals are consistent § Ratio – interval, plus ratios are consistent, true zero Bluman Chapter 1 5  z More Explanation! § Nominal – classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data. Ex. names, colors, marital status,… etc. § Ordinal – classifies data into categories that can be ranked; however, precise differences between the ranks do not exist. Ex. letter grades (A, B, C, D, F), the bag sizes (small, medium, or large) ,… etc. Bluman Chapter 1 6  z More Explanation! § Interval – ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero. Ex. Temperature, since there is a meaningful difference of 1 F between each unit, such as 72 and 73 F. But There is no true zero. 0 F does not mean no heat at all. Bluman Chapter 1 7  z More Explanation! § Ratio – possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same variable is measured on two different members of the population. Ex. height, weight, area, and number of phone calls received. Ratio scales have differences between units (1 inch, 1 pound, etc.) and a true zero. Zero pound means no weight. Bluman Chapter 1 8 z Determine the measurement level? Variable Nominal Ordinal Interval Ratio Level Hair Color Zip Code Letter Grade ACT Score Height Age Temperature (F) Bluman Chapter 1 9 z Answer! Variable Nominal Ordinal Interval Ratio Level Hair Color ✔ Nominal Zip Code ✔ Nominal Letter Grade ✔ Ordinal ACT Score ✔ Interval Height ✔ Ratio Age ✔ Ratio Temperature (F) ✔ Interval Bluman Chapter 1 10 z More detailed Answer with possipilities! Variable Nominal Ordinal Interval Ratio Level Hair Color Yes No Nominal Zip Code Yes No Nominal Letter Grade Yes Yes No Ordinal ACT Score Yes Yes Yes No Interval Height Yes Yes Yes Yes Ratio Age Yes Yes Yes Yes Ratio Temperature (F) Yes Yes Yes No Interval  z Some Sampling Techniques § Random – is a sample in which all members of the population have an equal chance of being selected. For Example, a class of 200 students is numbered from 1 to 200, and 60 students are randomly chosen from the class. Bluman Chapter 1 12  z Some Sampling Techniques Some Sampling Techniques Bluman Chapter 1 13  z Some Sampling Techniques § Systematic – is a sample obtained by selecting every kth member of the population where k is a counting number. For example, in a factory producing television sets, every 100th set produced is inspected. Bluman Chapter 1 14  z Some Sampling Techniques Some Sampling Techniques Bluman Chapter 1 15  z Some Sampling Techniques § Stratified – is a sample obtained by dividing the population into subgroups or strata according to some characteristic relevant to the study. Then subjects are selected from each subgroup. For example, a class of 200 students the students have different class rankings (freshmen, sophomore, junior, and senior). A random sample from each class ranking is taken. Bluman Chapter 1 16  z Some Sampling Techniques Some Sampling Techniques Bluman Chapter 1 17  z Some Sampling Techniques § Cluster – is obtained by dividing the population into sections or clusters and then selecting one or more clusters and using all members in the cluster(s) as the members of the sample. For example, an airline company randomly chooses four flights from a list of all flights taking place that day. All passengers on the selected flights are asked to fill out a survey on meal satisfaction. Bluman Chapter 1 18  z Some Sampling Techniques Some Sampling Techniques Bluman Chapter 1 19  z Some Sampling Techniques § Convenient – a researcher uses subjects who are convenient. Example, mall surveys. Bluman Chapter 1 20  z Some Sampling Techniques § Sampling error – is the difference between the results obtained from a sample and the results obtained from the population from which the sample was selected. For example, suppose you select a sample of full-time students at your college and find 56% are female. Then you go to the admissions office and get the genders of all full-time students that semester and find that 54% are female. The difference of 2% is said to be due to sampling error. Bluman Chapter 1 21 z See You Next Time!