What are Summary statistics? A statistics summary gives information about the data in a sample. It can help understand the values better. It may include the total number of values, minimum value, and maximum value, along with the mean value and the standard deviation corresponding to a data collection. With this, you can understand the trends, outliers, and distribution of values in a data set. This is especially useful when dealing with large amounts of data as it can help in analyzing the data better. This information can be utilized to steer the rest of the analysis and derive more information about a data set. These are values that are calculated based on the sample data and do not go beyond the data on hand.
By definition, the summary statistics sum up the features of a data sample. They describe the values and provide related measurements. These work as a basis for understanding the values recorded during a study.
Descriptive statistics can show where the mean of a set of values lies. It can also help to understand if the data is skewed. Descriptive or summary statistics include:
What is the meaning of summary statistics? It can be better understood with the help of the following illustrations:
Every summary statistics example quoted above focuses on one of the important aspects- the mean, the variability, or the data distribution.
The summary or descriptive statistics can be drilled down into different types, measures, or features. With a focus on averages, the description or summary can be focused on any of the three main categories: 1). the measure of the average value; 2) the frequency of each value; or 3) the spread of the values.
Also referred to as central tendency, this summary shows or describes a data set’s center or average. This is measured by the calculated values of the mean, median, and mode.
Mean: This is the most common method of calculating the average value. Usually represented by ‘M.’ The mean can be found by adding the values of the responses and then dividing this sum by the total number of responses (denoted by N). Consider this – a person wants to find out the number of hours they work in one week per day. The data set would include entries of the hours clocked every day of that week – 8, 10, 7, 9, 8, 6, and 4. 52 would be the sum of all these entries, and the total number of responses would be 7. 52 divided by 7 would give the value of M, which is 7.4.
Median: This is defined as the exact central value in the data set. By arranging the values from the lowest to the highest, we get 8 as the median, with 3 values to its left and 3 values to its right.
Mode: This represents the most frequent value in a data set. A given data set may have many modes, including 0 (zero). The mode can be found by arranging the values in a data set in ascending order and then looking for values that are repeated. In the example of work hours per week, by arranging the values from the lowest 4 to the highest 10, we can see that the value 8 is repeating. Thus 8 is the mode.
The measure of spread is also referred to as Dispersion, Variability, or Frequency Distribution. This measure helps us understand how the responses are spread out. The three aspects of spread are range, SD (Standard Deviation), and Variance. Let us examine each of these to understand what the summary statistics meaning is:
Range: This can be used to understand how far the highest and lowest values lie in a data set. This can be found by the subtraction of these two values (i.e., highest – lowest). Considering the earlier example of working hours, the highest entry was 10 and the lowest 4. The range would be 10-4=6.
Standard Deviation: This is an indication of the average variability of the data set. This shows how far each value lies from the value of M, the mean. The higher the value, the more variability. There are several steps to arrive at the SD:
Values of a data set and related observations can be represented graphically in tons of ways. Common graphs and chart types include histograms, Bar charts, Box plots, Frequency Distribution Tables, Scatter Plots, and Pie charts. Each of these comes with its own benefits and can be chosen based on how well it represents the data and how easily a person can understand the meaning of summary statistics via the representation.
The applications are far and wide and include an assortment of fields and professions – from academics, finance and investments, or even government organizations. Economic interests may lie in data pertaining to consumer spending, inflation, changes in the GDP, and more.
Analysts involved in the Finance domain could be interested in companies and industries, market information with a focus on volumes and prices, consumer sentiment regarding a product or service, and many more variables.
Due to its focus on the collected data, descriptive and summary statistics may seem limited at first glance. However, they aid an analyst in quantifying the data set on hand and help chalk out its basic characteristics. Plus, post-data collection involves no uncertainties; these work well for cleaning up large amounts of data. Along with organized and simplified data, the descriptions or summary statistics thus obtained set the stage for further data analysis.
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