Northcentral University Descriptive and Inferential Statistics Discussion
Describe the differences between descriptive and inferential statistics. Then, give a short summary of measures of central tendency, standard deviation, and how they are related.
Respond to this:
There are in general two branches of statistical studies. The first type of statistical study that will be discussed is descriptive. Descriptive statistics is when you gather, sort, and summarize data from samples. In this type of statistical study the researcher is describing something, and not necessarily drawing a conclusion. In other words ‘presenting the data’. With inferential statistics however, the goal is to use descriptive statistics (data) to estimate population parameters and ‘draw a conclusion’. Note, that I used the word ‘estimate’ possible parameters. It’s highly unlikely that a researcher would be able to obtain an entire population’s parameters. For instance, it would be impossible to ask every woman in the country diagnosed with cervical cancer; if they’d prefer chemotherapy or radiation?” It’s quite impossible to survey or ask millions of people. Therefore, we as researchers look at populations, take a sample and gather all the information and use descriptive statistics to analyze the data collected.
Based on a phone survey, 24% of all women prefer radiation. This is a type of inferential statistics because a conclusion has been drawn by using descriptive statistics data to estimate the parameters of a population. In this case the population is all women. The parameters is what percentage of women prefer radiation. Again being that it is impossible to survey everyone in the United States a sample would be used. On the other hand, 55% of women at a local health clinic diagnosed with cancer plan on receiving chemotherapy. Looking at this example there is no inference ‘conclusion’ being drawn making this a type of descriptive statistics. This example is simply presenting a fact; that fact being 55% of women in a local clinic plan on using chemotherapy versus radiation.
The center of a bunch of data points is typically a good example of some type of data we can expect from the group as a whole. The most frequently used measures of central tendency is mean, median, and mode. The mean is the average or expectancy that takes all the numbers in a data set, and divides the values by the number of data points present. The mean measures values that are usually normally distributed. A normal distribution of data that has approximately an equal amount of data on either side of the middle, and the most common values being around the middle. The median however is the middle number if the data was lined up in ascending order (smallest -> largest). Lastly, the mode is the value that appears the most frequent in a data set. This central measurement is most useful when there is a large sample; therefore resulting in a large number of popular values. Standard deviation measures the variability of a set of data. A smaller standard deviation means less variability. In terms of probability the SD provides a base line for interpreting data. The standard deviation formula is represented below. In order to work out the problem and get the standard deviation, the mean must be calculated first. The mean, being apart of the central tendency measurements, indicates that one standard deviation cannot be without central tendency measurements.
2nd Response:
Descriptive Statistics is a discipline which is concerned with describing the population under study. (Key Differences, 2017)
This would be analyzing and calculating specific data. A good example is calculating my sons batting average for the 2019 Season once its complete.
Inferential Statistics is a type of statistics; that focuses on drawing conclusions about the population, on the basis of sample analysis and observation. (Key Differences, 2017). This would be observing the data and then providing a prediction. A good example would be if I was to predict my sons batting average for the 2019 season, while the 2019 baseball is not yet completed.
A measure of central tendency is a summary statistic that represents the center point or typical value of a data set (Frost, 2019). The three most common measures of central tendency are the mean, median, and mode.
The standard deviation is a measure of the spread of scores within a set of data.
The sample standard deviation formula is:
s = sample standard deviation = sum of…
= sample mean
n = number of scores in sample. (Laerd, 2019)
Third Response:
Descriptive versus inferential statistics
Descriptive statistics defines and summarizes the population sample being studied by utilizing charts, graphs, and tables to analyze and display the data described in a meaningful manner (Taylor, 2012).
Inferential statistics allows the researcher to come to assumptions about the study population using comparison, testing, and probability to envisage conclusions constructed on observation and sample analysis (Taylor, 2012).
Measures of central tendency
This is a summary statistic representing the center point of a dataset commonly calculated as the mean, median, and mode (Frost, 2018). The mean is the mathematical average of the dataset (Frost, 2018). The mean of the population (N) is μ “mu”, but the mean of the sample(n) is written as x̅ “x-bar”(Brown, 2018). The median is the actual center of the data meaning half the numbers are less than or equal to it and the rest are greater than or equal to it (Frost, 2018). The statistical symbol for the sample (n) is M or Med or x̃ “x-tilde” (Brown, 2018). The mode is the value that occurs most frequently in the data set, If no value repeats then the data set has no mode (Frost, 2018). The symbol for mode can be written Mo.
If you have the data set 1,2,4,6,4
I always start by listing my data set in numerical order = 1,2, 4, 4, 6
Mean= add the set 1+2+4+4+6= 17 then divide by number in the set 17/5 = 3.4 so μ = 3.4
In this example the median and mode both = 4
Standard deviation
Standard deviation (σ or SD) is one of the four measures of spread, the other three being range, interquartile range (IQR), and variance (Brown, 2018). These terms all summarize the data by describing how spread out the scores are (Brown, 2018). Standard deviation (σ or SD) is the square root of the variance (s² or σ²), which is the squared differences from the mean.
I have found a nifty site that does what my daughter used to call the scary math for me. It is https://www.calculator.net/standard-deviation-calculator.html I love this site because it does the calculations but it also shows step by step how to get the answer.
Looking at the formula for standard deviation, it is clear that measures of central tendency is needed to calculate the disbursement of the data.
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