How to find third quartile from frequency distribution table given coefficient skewness, median, mean and first quartile respectively
Answers
Answer:
Contents (click to skip to the page section):
Solving by hand:
Solve the formula by hand (odd set of numbers).
What if I have an even set of numbers?
Find an interquartile range for an odd set of numbers: Second Method
Box Plot interquartile range: How to find it
Using Technology:
Interquartile Range in Minitab
Interquartile Range in Excel
Interquartile Range in SPSS
Interquartile Range on the TI83
Q1, Q3 and the IQR on the TI89
General info:
What is an Interquartile range?
What is the Interquartile Range Formula?
IQR as a Test for Normal Distribution
What is an Interquartile Range used for?
History of the Interquartile Range.
Solve the formula by hand.
Watch the video or read the steps below:
Steps:
Step 1: Put the numbers in order.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 2: Find the median.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 3: Place parentheses around the numbers above and below the median.
Not necessary statistically, but it makes Q1 and Q3 easier to spot.
(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).
Step 4: Find Q1 and Q3
Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.
(1, 2, 5, 6, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.
Step 5: Subtract Q1 from Q3 to find the interquartile range.
18 – 5 = 13.
Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step explanations, just like this one!
What if I Have an Even Set of Numbers?
Example question: Find the IQR for the following data set: 3, 5, 7, 8, 9, 11, 15, 16, 20, 21.
Step 1: Put the numbers in order.
3, 5, 7, 8, 9, 11, 15, 16, 20, 21.
Step 2: Make a mark in the center of the data:
3, 5, 7, 8, 9, | 11, 15, 16, 20, 21.
Step 3: Place parentheses around the numbers above and below the mark you made in Step 2–it makes Q1 and Q3 easier to spot.
(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21).
Step 4: Find Q1 and Q3
Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data.
(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.
Step 5: Subtract Q1 from Q3.
16 – 7 = 9.
This is your IQR.
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Find an interquartile range for an odd set of numbers: Alternate Method
As you may already know, nothing is “set in stone” in statistics: when some statisticians find an interquartile range for a set of odd numbers, they include the median in both both quartiles. For example, in the following set of numbers: 1,2,5,6,7,9,12,15,18,19,27 some statisticians would break it into two halves, including the median (9) in both halves:
(1,2,5,6,7,9),(9,12,15,18,19,27)
This leads to two halves with an even set of numbers, so you can follow the steps above to find the IQR.
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Box Plot interquartile range: How to find it
Watch the video or read the steps below:
Box Plot interquartile range: How to find it
box plot interquartile range
Example question: Find the interquartile range for the above box plot.
Step 1: Find Q1.Q1 is represented by the left hand edge of the “box” (at the point where the whisker stops).
finding q1 on the boxplot graph
In the above graph, Q1 is approximately at 2.6. (A complete explanation of Q1 is here: The five number summary.)
Step 2: Find Q3.
Q3 is represented on a boxplot by the right hand edge of the “box”.
finding q3 on the boxplot
Q3 is approximately 12 in this graph.
Step 3: Subtract the number you found in step 1 from the number you found in step 3.
This will give you the interquartile range. 12 – 2.6 = 9.4.
That’s it!
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Interquartile Range in Minitab
Read on for step-by-step directions, or view the video version below.
Interquartile Range in Minitab: Steps
Example question: Find an interquartile range in Minitab for the Grade Point Average (GPA) in the following data set:
Grade Point Average (GPA): 1(3.2), 1(3.1), 2(3.5), 2(2.0), 3(1.9), 3(4.0), 3(3.9), 4(3.8), 4(2.9), 5(3.9), 5(3.2), 5(3.3), 6(3.4), 6(2.6), 6(2.5), 7(2.0), 7(1.5), 8(4.0), 8(2.0).
Step 1: Type your data into a Minitab worksheet. Enter your data into one or two columns.
minitab interquartile range a
Step 2: Click “Stat,” then click “Basic Statistics,” then click “Display Descriptive Statistics” to open the Descriptive Statistics menu.
minitab interquartile range b
Step 3: Click a variable name in the left window and then click the “Select” button to transfer the variable name to the right-hand window.
Step 4: Click the “Statisti