Elementary Statistics
Statistics refers to the set of procedures involved in preparing research, conducting experiments, acquiring data, arranging it, summarizing, and presenting, analyzing, and interpreting data. Elementary Statistics is a broad study area and has its foundation in descriptive statistics, probability, probability distribution, planning and analyzing experiments, regression analysis and correlation coefficients, and tables. Descriptive statistics explain data such as interquartile range and mean. Probability expresses the possibility of an occurrence. For instance, raining on a certain day or winning an election, etc.
Probability distributions subject students to learning about data graphs, for example, normal distribution graphs, otherwise known as the bell curves. Planning and analyzing is the stage of elementary statistics that allows scholars to decide whether the results of studies are logical. The regression analysis and correlation coefficients are the topics of elementary statistics that deal with graphs such as scatter plots used to put data into equations. Under this topic, future trends are also discussed. Under elementary data, you will also get to use tables like z-tables and t-table. It is worth noting that tables provide much information concerning probabilities and data distributions.
Frequency Distribution and its importance in Elementary Statistics
Frequency distribution refers to how values are distributed within a set of data. It is the first step in data analysis and is important because it shows the most suited measure of the location to apply. For instance, the arithmetic mean provides a suitable summary measure in a case where values are symmetrically distributed. A frequency distribution can also indicate “odd” points for special attention in the data verification process. It can enable you to assess any criteria used to divide polymodal distributions by exposing them. Determination of the most suitable statistical analysis may be arrived at via frequency distribution. It is worth noting that understanding frequency distribution is vital in interpreting the behavior of statistics and understanding statistical inference.
Types of Variables in Elementary Statistics
There are many types of variables in elementary statistics. These variables include nominal variables, ordinal variables, measurement variables, continuous variables, and discrete variables. However, the most recognized types of variables are continuous and discrete variables. Statistically, a continuous variable can be defined as a random sample with no two identical values. In other words, it can, between its maximum and minimum value, take any intermediate value. On the other hand, In a discrete or a merit variable, the measurement can only exist as an integer (a whole number)—for instance, the number of congregants in a church or the number of vehicles in parking.
Quantiles
A quantile is a location within a set of ranked numbers, below which a certain proportion, p, of that set lie. For instance, take these 4 numbers arranged in ascending order into consideration;
|
egg weight (mg): |
0.1 |
1.5 |
3.7 |
9.4 |
|
p = 0.5 |
⇑ |
|||
Under the definition above, if p is 0.5, half of the observations lie below a value - the 0.5th quantile - commonly known as the median. The median lies somewhere between the second and third-ranked values (1.5 and 3.7). Note that, as long as we have four values, the 0.5th quantile would be positioned between the second and third positioned values irrespective of what their values happen to be. In other words, quantiles describe the relative rank. There are two ways to work with quantiles; through the calculation of the value corresponding to the rank of a predefined, pth quantile, or if you are provided with the rank of a certain value within a set of t values can calculate p.
Definition of Some Basic Terms in Elementary Statistics
Data: It refers to the raw information that has been gathered. For instance, observations made on genders, measurements, or survey responses.
Sample: A sub-collection was used to represent the rest of the gathered data.
The nominal level of measurement is data made up of only names, categories, or labels.
Ordinal level of measurement: Data that can be arranged in a certain order; however, the difference between data values is meaningless or cannot be determined.
Sampling error: Refers to the difference between the actual population result and the sample result, that is, the error resulting from chance sample fluctuations.
