Statistics - Foster
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| 🇬🇧 | 🇬🇧 |
| Symbol N - Uppercase N | Represents the population size. If a population is a class containing 20 students, and in a random sample of 5 of these students we find 2 freshmen, then the population size is uppercase N=20. |
| Parameter | A number that provides information about a population. We might collect all the ages of students at Wylie campus. The mean (average) of those ages would be a parameter. Also, the proportion of students who are less than 6 feet tall would be a parameter. |
| Qualitative variables | Do not have numbers that can be added and subtracted in a meaningful way. They typically report qualities, or characteristics. |
| Symbol N (Uppercase N) | Represents the population size. If a population is a class containing 20 students, and in a random sample of 5 of these students we find 2 freshmen, then the population size is N=20. |
| Symbol N (Uppercase N) | Represents the population size. If a population is a class containing 20 students, and in a random sample of 5 of these students we find 2 freshmen, then the population size is N=20. |
| Population | The set of all individuals to be studied. If you want to study all students at Wylie Campus, then the population is all students at Wylie Campus. |
| Sample | A part of a population. A subset of individuals from a population. If your population is all students at Wylie Campus, then a sample from that population must include some of the students from Wylie Campus. The sample may only contain students from Wylie Campus. |
| Parameter | A number that provides information about a population. We might collect all the ages of students at Wylie campus. The mean (average) of those ages would be a parameter. Also, the proportion of students who are less than 6 feet tall would be a parameter. |
| Statistic | A number that provides information about a sample. If we randomly select 10 students from Wylie campus and record their ages, then he mean (average) of those 10 ages would be a statistic. Also, the proportion of the 10 students who are less than 6 feet tall would be a statistic. |
| Descriptive Statistics | The field of descriptive statistics endeavors to describe a characteristic of individuals in a sample. The descriptions could be graphs, numbers, tables, etc. |
| Inferential Statistics | The field of inferential statistics takes data from a sample and uses that data along with probability to draw conclusions (make inferences) about the population. Whenever the conclusions from inferential statistics are reported, a measure of reliability must be included. |
| Measures of Reliability | We will use the level of confidence and the significance level as our measures of reliability. If a report states that the population proportion is between 0.15 and 0.18 with 95% confidence, then the confidence level is 95%. Typically, the significance level is 100% minus the confidence level. In this example with 95% confidence, the two sided significance level would be 5%. |
| Quantitative variables | Have numbers that can be added and subtracted in a meaningful way. Height and Weight are good examples. |
| Qualitative variables | Do not have numbers that can be added and subtracted in a meaningful way. They typically report qualities, or characteristics. Nationality and grade level (freshman, sophomore, etc.) are good examples. |
| Continuous variables | A quantitative variable can be continuous or discrete. A continuous variable may take on any value including fractions and decimals. Height and Weight are good examples since you can be 60 and a half inches tall, or you can weigh 54.2 kilograms. |
| Discrete variables | A quantitative variable can be continuous or discrete. A discrete variable may take on any whole number value. A discrete variable may never have fractions or decimals. The "number of children" per class is a discrete variable since you may never have half of a child. |
| Frequency | The frequency of a characteristic is the number of times that the characteristic appears amongst the individuals. An example would be a class that contains 22 freshmen and 8 sophomores yields the frequency of freshmen is 22. |
| Relative frequency | The relative frequency of a characteristic is the proportion that the characteristic appears amongst the individuals. An example would be a class that contains 22 freshmen and 8 sophomores yields the relative frequency of freshmen is 22/30=0.733. |
| Mean | The mean is the balance point of a data set. It is calculated by adding all the values and dividing that total by the number of data values. The mean of {1,2,6} is (1+2+6)/3 = 3 |
| Median | The median separates the lowest 50% of data values from the highest 50% of data values. To calculate the median, think of it as the "middle" number. The median of the data set {1,2,6} is 2 because 2 is the middle number. However, if there is an even number of data values, we must average the 2 middle numbers. The median of the data set {1,2,6,7} is (2+6)/2=4. |
| Mode | The mode is the most frequent number. In the data set {1,2,3,3}, the mode is 3. In the data set {1,2,2,3,3} there are two modes and the modes are 2 and 3. In the data set {1,2,3} there is no mode because no data value occurs more than once. |
| Percentile | A percentile reports the percentage of data values that are less than or equal to a given number. For example, on a Biology quiz, Jose scored at the 90th percentile. We know that 90% of the grades on the Biology quiz were less than or equal to Jose's score. Only 10% of the grades were higher than Jose's score. |
| Quartile | A quartile is a special percentile. Q1 is the first quartile which is equal to the 25th percentile. Q2 is the second quartile which is equal to the 50th percentile which is equal to the median. Q3 is the third quartile which is equal to the 75th percentile. If Jose scored at the third quartile on his English essay, then we know that 75% of the grades on the English essays were less than or equal to Jose's score. Only 25% of the grades on the English essays were higher than Jose's score. |
| Range | The distance between the lowest and highest values in a data set. In the data set {1,2,3,4,5} the range is 4. In the data set {1,2,3,10} the range is 9. In the data set {1,1,1,1,1} the range is 0. When the range of a data set is 0, we know that all of the values in the data set must be the same value. |
| Interquartile range | The interquartile range reports the range of the middle 50% of data values. It is the distance between the first and third quartiles. It helps us to understand how spread out the data values are. On a quiz, the grades were {71, 82, 85, 85, 87, 91, 93, 95, 98, 98, 100} The range is 100-71=29, but the first quartile is 85 and the third quartile is 98, making the interquartile range 98-85=13. The middle 50% of data values cover a range of 13 points. |
| Symbol x - lower case x | Represents either a data value, or sometimes a count of successes. If the data values are measuring height, then the value of x will be a height. If the data values are counting the number of freshmen, then the value of x will be the count of freshmen. |
| Symbol p - lower case p | Represents the population proportion. If a population is a class containing 20 students, and in the class there are 15 freshmen, then the population proportion is lower case p=15/20=0.75. |
| Symbol p-hat | Represents the sample proportion. If a population is a class containing 20 students, and in a random sample of 5 of these students we find 2 freshmen, then the sample proportion is p-hat=4/5=0.8. |
| Symbol n - lower case n | Represents the sample size. If a population is a class containing 20 students, and in a random sample of 5 of these students we find 2 freshmen, then the sample size is lower case n=5. |
| Symbol N (Uppercase N) | Represents the population size. If a population is a class containing 20 students, and in a random sample of 5 of these students we find 2 freshmen, then the population size is N=20. |
| Symbol P - uppercase P | Represents the probability of an event. If a bag of marbles contains 5 red and 15 blue, then the probability of randomly selecting a red marble is uppercase P=5/20=0.25 |