Complete the following steps to interpret display descriptive statistics. Key output includes N, the mean, the median, the standard deviation, and several graphs.
In This Topic
Step 1: Describe the size of your sample
Step 2: Describe the center of your data
Step 3: Describe the spread of your data
Step 4: Assess the shape and spread of your data distribution
Step 5. Compare data from different groups
Step 1: Describe the size of your sample
Use N to know how many observations are in your sample. Minitab does not include missing values in this count.
You should collect a medium to large sample of data. Samples that have at least 20 observations are often adequate to represent the distribution of your data. However, to better represent the distribution with a histogram, some practitioners recommend that you have at least 50 observations. Larger samples also provide more precise estimates of the process parameters, such as the mean and standard deviation.
Statistics
Variable
N
N*
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
Torque
68
0
21.2647
0.778784
6.42202
10
16
20
24.75
37
Step 2: Describe the center of your data
Use the mean to describe the sample with a single value that represents the center of the data. Many statistical analyses use the mean as a standard measure of the center of the distribution of the data.
The median is another measure of the center of the distribution of the data. The median is usually less influenced by outliers than the mean. Half the data values are greater than the median value, and half the data values are less than the median value.
The median and the mean both measure central tendency. But unusual values, called outliers, can affect the median less than they affect the mean. If your data are symmetric, the mean and median are similar.
Symmetric
Not symmetric
Statistics
Variable
N
N*
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
Torque
68
0
21.2647
0.778784
6.42202
10
16
20
24.75
37
Step 3: Describe the spread of your data
Use the standard deviation to determine how spread out the data are from the mean. A higher standard deviation value indicates greater spread in the data.
Statistics
Variable
N
N*
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
Torque
68
0
21.2647
0.778784
6.42202
10
16
20
24.75
37
Step 4: Assess the shape and spread of your data distribution
Use the histogram, the individual value plot, and the boxplot to assess the shape and spread of the data, and to identify any potential outliers.
Examine the spread of your data to determine whether your data appear to be skewed
When data are skewed, the majority of the data are located on the high or low side of the graph. Often, skewness is easiest to detect with a histogram or boxplot.
Right-skewed
Left-skewed
Determine how much your data varies
Assess the spread of the points to determine how much your sample varies. The greater the variation in the sample, the more the points will be spread out from the center of the data.
Look for multi-modal data
Multi-modal data have multiple peaks, also called modes. Multi-modal data often indicate that important variables are not yet accounted for.
If you have additional information that allows you to classify the observations into groups, you can create a group variable with this information. Then, you can create the graph with groups to determine whether the group variable accounts for the peaks in the data.
Simple
With Groups
Identify outliers
Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.
Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, one-time events (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.
The mode is the most commonly occurring number in the data set. The mode is best used when you want to indicate the most common response or item in a data set.
There are several ways of presenting descriptive statistics in your paper. These include graphs, central tendency, dispersion and measures of association tables. Graphs: Quantitative data can be graphically represented in histograms, pie charts, scatter plots, line graphs, sociograms and geographic information systems.
Descriptive statistics is essentially describing the data through methods such as graphical representations, measures of central tendency and measures of variability. It summarizes the data in a meaningful way which enables us to generate insights from it.
If you've collected data on more than one variable, you can use bivariate or multivariate descriptive statistics to explore whether there are relationships between them. In bivariate analysis, you simultaneously study the frequency and variability of two variables to see if they vary together.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.
Examples of metrics used in descriptive analytics include year-over-year pricing changes, month-over-month sales growth, the number of users, or the total revenue per subscriber.
The purpose of a descriptive statistic is to summarize data. Descriptive stats only make statements about the set of data from which they were calculated; they never go beyond the data you have.
It represents the typical distance between each data point and the mean. Smaller values indicate that the data points cluster closer to the mean—the values in the dataset are relatively consistent. Conversely, higher values signify that the values spread out further from the mean.
Data interpretation is the process of reviewing data and arriving at relevant conclusions using various analytical research methods. Data analysis assists researchers in categorizing, manipulating data, and summarizing data to answer critical questions. LEARN ABOUT: Level of Analysis.
Data interpretation refers to the process of using diverse analytical methods to review data and arrive at relevant conclusions. The interpretation of data helps researchers to categorize, manipulate, and summarize the information in order to answer critical questions.
Descriptive statistics summarize and describe the main features of a dataset through measures like mean, median, and standard deviation, providing a quick overview of the sample data.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.
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