How to find the first quartile of a data set

1. First Quartile(Q1) = ((n + 1)/4)th Term.
2. Second Quartile(Q2) = ((n + 1)/2)th Term.
3. Third Quartile(Q3) = (3(n + 1)/4)th Term.

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.

How do you find Q1 in a set of data?

Q1 is the middle value in the first half of the data set. Since there are an even number of data points in the first half of the data set, the middle value is the average of the two middle values; that is, Q1 = (3 + 4)/2 or Q1 = 3.5.

How do you find the quartiles of a data set?

1. Order your data set from lowest to highest values.
2. Find the median. This is the second quartile Q2.
3. At Q2 split the ordered data set into two halves.
4. The lower quartile Q1 is the median of the lower half of the data.
5. The upper quartile Q3 is the median of the upper half of the data.

What is the Q1 of a data set?

The lower quartile, or first quartile, is denoted as Q1 and is the middle number that falls between the smallest value of the dataset and the median. The second quartile, Q2, is also the median.

How do you calculate Q1 Q2 and Q3?

1. Formula for Lower quartile (Q1) = N + 1 multiplied by (1) divided by (4)
2. Formula for Middle quartile (Q2) = N + 1 multiplied by (2) divided by (4)
3. Formula for Upper quartile (Q3) = N + 1 multiplied by (3) divided by (4)
4. Formula for Interquartile range = Q3 (upper quartile) – Q1 (lower quartile)

How do I find the lower quartile?

To find the lower quartile of a set of data, we can find the median of the data and then find the median of the first half. This strategy is similar to dividing a cake into halves, and then dividing one of the halves in half so that you end up with a quarter of the cake.

What are the steps to find the lower and upper quartiles of a data set?

Arrange the data in ascending order (low to high). This will be {x1,x2,x3,…,xn}. C) Find the position numbers that correspond to the 25th and 75th percentiles (a.k.a. the lower and upper quartiles). The pth percentile of a data set is an element (derived from the data set) that is greater than p% of the data set.

How is quartile calculated?

The quartile measures the spread of values above and below the mean by dividing the distribution into four groups. A quartile divides data into three points—a lower quartile, median, and upper quartile—to form four groups of the dataset.

How do you find upper and lower quartile?

In order to calculate this value we must first understand what the lower quartile, median and upper quartile are: the lower quartile is the median of the lower half of the data. The. the upper quartile is the median of the upper half of the data.

What is the lower quartile equal to?

The first quartile (or lower quartile), Q1, is defined as the value that has an f-value equal to 0.25. This is the same thing as the twenty-fifth percentile. The third quartile (or upper quartile), Q3, has an f-value equal to 0.75. The interquartile range, IQR, is defined as Q3-Q1.

How do you find the 1st and 3rd quartile in Excel?

1. Type your data into a single column. For example, type your data into cells A1 to A10.
2. Click an empty cell somewhere on the sheet. For example, click cell B1.
3. Type “=QUARTILE(A1:A10,1)” and then press “Enter”. This finds the first quartile. To find the third quartile, type “=QUARTILE(A1:A10,3)”.

How many quartiles does a data set have?

The quartiles break up a data set into four parts, with roughly 25 percent of the data being less than the first quartile, 25 percent being between the first and second quartile, 25 percent being between the second and third quartile, and 25 percent being greater than the third quartile.

What is Q1 Q2 Q3 in statistics?

Q1 is the “middle” value in the first half of the rank-ordered data set. Q2 is the median value in the set. Q3 is the “middle” value in the second half of the rank-ordered data set.

How do you find Q1 Q2 Q3 in Excel?

The IQR is a measure of the middle dispersion of a dataset, basically the difference between Q1 and Q3. To calculate the IQR in Microsoft Excel, use the =QUARTILE function to calculate Q1 and Q3, and ultimately find the difference between these two values.

How do you find the 1st quartile?

1. First Quartile(Q1) = ((n + 1)/4)th Term.
2. Second Quartile(Q2) = ((n + 1)/2)th Term.
3. Third Quartile(Q3) = (3(n + 1)/4)th Term.

Quartiles are the values that divide a list of numbers into quarters:

• Put the list of numbers in order
• Then cut the list into four equal parts
• The Quartiles are at the "cuts"

Like this:

Put them in order: 2, 4, 4, 5, 6, 7, 8

Cut the list into quarters:

And the result is:

• Quartile 1 (Q1) = 4
• Quartile 2 (Q2), which is also the Median, = 5
• Quartile 3 (Q3) = 7

Sometimes a "cut" is between two numbers ... the Quartile is the average of the two numbers.

The numbers are already in order

Cut the list into quarters:

In this case Quartile 2 is half way between 5 and 6:

Q2 = (5+6)/2 = 5.5

And the result is:

• Quartile 1 (Q1) = 3
• Quartile 2 (Q2) = 5.5
• Quartile 3 (Q3) = 7

Interquartile Range

The "Interquartile Range" is from Q1 to Q3:

To calculate it just subtract Quartile 1 from Quartile 3, like this:

The Interquartile Range is:

Q3 − Q1 = 7 − 4 = 3

Box and Whisker Plot

We can show all the important values in a "Box and Whisker Plot", like this:

A final example covering everything:

4, 17, 7, 14, 18, 12, 3, 16, 10, 4, 4, 11

Put them in order:

3, 4, 4, 4, 7, 10, 11, 12, 14, 16, 17, 18

Cut it into quarters:

3, 4, 4 | 4, 7, 10 | 11, 12, 14 | 16, 17, 18

In this case all the quartiles are between numbers:

• Quartile 1 (Q1) = (4+4)/2 = 4
• Quartile 2 (Q2) = (10+11)/2 = 10.5
• Quartile 3 (Q3) = (14+16)/2 = 15

Also:

• The Lowest Value is 3,
• The Highest Value is 18

So now we have enough data for the Box and Whisker Plot:

And the Interquartile Range is:

Q3 − Q1 = 15 − 4 = 11

Copyright © 2019 MathsIsFun.com

Find the quartiles of this data set: 6, 47, 49, 15, 43, 41, 7, 39, 43, 41, 36.

You first need to arrange the data points in increasing order. As you do so, you can give them a rank to indicate their position in the data set. Rank 1 is the data point with the smallest value, rank 2 is the data point with the second-lowest value, etc.

Table summary
This table displays the results of Rank of data points. The information is grouped by Rank (appearing as row headers), Value (appearing as column headers).

Then you need to find the rank of the median to split the data set in two. As we have seen in the section on the median, if the number of data points is an uneven value, the rank of the median will be

(n + 1) ÷ 2 = (11 + 1) ÷ 2 = 6

The rank of the median is 6, which means there are five points on each side.

Then you need to split the lower half of the data in two again to find the lower quartile. The lower quartile will be the point of rank (5 + 1) ÷ 2 = 3. The result is Q1 = 15. The second half must also be split in two to find the value of the upper quartile. The rank of the upper quartile will be 6 + 3 = 9. So Q3 = 43.

Once you have the quartiles, you can easily measure the spread. The interquartile range will be Q3 - Q1, which gives 28 (43-15). The semi-interquartile range is 14 (28 ÷ 2) and the range is 43 (49-6).