With this in mind, the five-number summary consists of the following:
- The minimum – this is the smallest value in our data set.
- The first quartile – this number is denoted Q1 and 25% of our data falls below the first quartile.
- The median – this is the midway point of the data. ...
- The third quartile – this number is denoted Q3 and 75% of our data falls below the third quartile.
How to calculate 5 number summary?
Calculating the five-number summary involves finding the observations for each quartile as well as the minimum and maximum observed values from the data sample. If there is no specific value in the ordered data sample for the quartile, such as if there are an even number of observations and we are trying to find the median, then we can calculate the mean of the two closest values, such as the two middle values.
What does a five number summary tell you?
What is a Five Number Summary?
- Lower Extreme (Minimum) The lower extreme, also known as the minimum, is a descriptive statistic that represents the smallest number within the data set.
- Lower Quartile. The lower quartile, also known as Quartile 1, is a deceptive statistic that represents the number in the middle of the lower half of the data set.
- Median. ...
- Upper Quartile. ...
How do you find a 5 number summary?
What is the five number summary in math?
- Put your numbers in ascending order (from smallest to largest).
- Find the minimum and maximum for your data set.
- Find the median.
- Place parentheses around the numbers above and below the median.
- Find Q1 and Q3.
How to find the five number summary in statistics?
With this in mind, the five-number summary consists of the following:
- The minimum – this is the smallest value in our data set.
- The first quartile – this number is denoted Q1 and 25% of our data falls below the first quartile.
- The median – this is the midway point of the data. ...
- The third quartile – this number is denoted Q3 and 75% of our data falls below the third quartile.
How do you find the 5 number summary?
How to Find a Five-Number Summary: StepsStep 1: Put your numbers in ascending order (from smallest to largest). ... Step 2: Find the minimum and maximum for your data set. ... Step 3: Find the median. ... Step 4: Place parentheses around the numbers above and below the median. ... Step 5: Find Q1 and Q3.More items...
What is a summary in math?
The information that gives a quick and simple description of the data. Can include mean, median, mode, minimum value, maximum value, range, standard deviation, etc.
What is a number Summary math?
in statistics, a summary of the distribution of a data set, i.e. minimum value, lower (1st) quartile, median (middle value), upper (3rd) quartile and the maximum value.
Which is not part of the five-number summary?
Heights of all elementary school children. Which of he following is not part of a five-number summary? The mean.
What is a summary measure?
A summary measure quantifies how much an outcome occurs within a single group, and a measure of effect quantifies how much an outcome differs between two groups.
What is a summary value?
Summary Values are evaluated on Summary entities (Parts, Planes, and Points) from the Design Study. They are used to compare important results quantities to evaluate the performance of design alternatives. Results are presented in a simple data table and plotted with bar graphs.
How do you explain summary statistics?
Summary statistics summarize and provide information about your sample data....Summary Statistics: Measures of locationMean (also called the arithmetic mean or average).Geometric mean (used for interest rates and other types of growth).Trimmed Mean (the mean with outliers excluded).Median (the middle of a data set).
What is meant by summary statistics?
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in. a measure of location, or central tendency, such as the arithmetic mean.
Why Are These Statistics in the 5-Number Summary?
Why does the 5-number summary contain these statistics instead of more familiar ones, such as the mean and standard deviation? These five statistics provide similar types of information as other statistics while having advantages over them.
Interpreting the Five-Number Summary
Let’s look at what these statistics tell you by working through an example dataset. For this example, we’ll look at body fat percentages in middle school girls. You might not be familiar with this subject area, but the 5-number summary can quickly help you get your bearings. You can download this CSV dataset: body_fat.
Boxplots Graphically Display the 5-Number Summary
Conveniently, boxplots display the 5-number summary in graphical form. The image below displays the boxplot for the body fat example. Notice how the five parts of the boxplot correspond to the summary values!
Reference
Hoaglin, David C.; Mosteller, Frederick; Tukey, John W., eds. (21 December 1982). Understanding Robust and Exploratory Data Analysis. Wiley Series in Probability and Statistics (1st ed.). Wiley.
What is a Five Number Summary?
The five-number summary is made up of five types of descriptive statistics: Lower Extreme, Lower Quartile, Median, Upper Quartile, and Upper Extreme.
What are the 5 numbers in the 5 number summary?
The 5 numbers in the five-number summary are lower extreme (minimum), the lower quartile (Q1) , the median (Q2) , the upper quartile (Q3) , and the upper extreme (maximum).
What is the median in statistics?
The median, also known as Quartile 2, is a descriptive statistic that represents the number in the middle of all the data within the data set.
What is the 9th data item?
Referring to our ordered list (4, 5, 6, 7, 8, 9, 13, 16, 19, 21, 24), we can see that the 9th data item is 19.
How many data points are in front of 9?
Looking at the data set, we can see that 9 is directly in the center. We can verify that by making sure there is the same number of data points in front of the 9 as there are behind the 9. There are 5 data points (4, 5, 6, 7, 8) that are in front of the 9 and another 5 data points (13, 16, 19, 21, 24) behind the 9. This verifies that 9 is directly in the center.
How many scales of measurement are there in a data set?
This means that the variables used within the data set must contain 1 of 3 possible scales of measurement.
Can you use all data sets to calculate a five number summary?
While most data sets can be used to calculate the five-number summary, not all data sets can be used. There are two requirements that must be in place to successfully calculate each of the 5 descriptive statistics within the five-number summary.
What is the Five Number Summary?
The five number summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3) and the maximum. The minimum is the smallest number, the maximum is the largest, the median is in the middle, Q1 is the median of the first half of the data and Q3 is the median of the second half.
5 Number Summary on a Box Plot
The 5 number summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3) and the maximum. On a box plot, the minimum and maximum are shown by the first and last lines respectively. The lower quartile is found where the box begins and the upper quartile is found where the box ends.
Example of Finding a Five Number Summary with an Even Set of Data
When finding the median of an even set of data, cross the same amount of numbers off at each end until two numbers remain in the middle. Then add these two numbers and divide by two. The same process is used when finding the lower quartile and upper quartile by finding the median of the first and second halves of the data respectively.
Outliers and the 5 Number Summary
An outlier is a value in a data set that is significantly different from the other values. An outlier is defined as any value that is more than 1.5×IQR below Q1 or more than 1.5× IQR above Q3.
What is a Five-Number Summary?
Five number summary: the five numbers that summarize the overall characteristics of a data set. These include the minimum, first quartile, median, third quartile, and maximum.
What is the median of a list?
The middle number of our list is the second 7 in the list. Therefore the median is 7. We will use this to separate the data set into a lower half (2, 3, 4, 5, 6, 6, 7) and an upper half (7, 7, 8, 9, 10, 11, 12).
Five number summary
The five-number summary gives you a rough idea about what your data set looks like. For example, you’ll have your lowest value (the minimum) and the highest value (the maximum) or more concentrated data.
How to enter data as a frequency table?
Simple. First-type data elements (separated by spaces or commas, etc.), then type f: and further write frequency of each data item. Each element must have a defined frequency that count of numbers before and after symbol f: must be equal. For example:
How to enter a grouped data?
Grouped data are data formed by aggregating individual data into groups so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.
How to enter data as a cumulative frequency table?
Similar to a frequency table, but instead f: type cf: in the second line. For example:
Questions
Question1: There seems to be a problem with the 5-figure calculator. I placed the following data set and the Q3, giving a wrong value. 8, 12, 9, 8, 16, 10 ,14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14. I used The program, against TI and Casio graphics calculator as well as a different program.
