how to find lower and upper quartile

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Data Set Prep

Calculating the Upper Quartile

Using Excel

Quartiles are numbers used to divide a set of data into four equal parts, or quarters.^[1] The upper quartile, or third quartile, is the top 25% of numbers in the data set, or the 75th percentile. The upper quartile is calculated by determining the median number in the upper half of a data set.^[ii] This value can exist institute by calculating with pen and newspaper, only y'all can also hands find the upper quartile using statistical software, such as MS Excel.

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Adapt the numbers of the data set in ascending gild. This ways ordering them from the smallest value to the largest value. Make sure to include all repeated values.^[3]
- For example, if your prepare of numbers is [iii, 4, 5, xi, 3, 12, 21, 10, 8, vii], you lot would reorder them like this: [iii, 3, 4, v, vii, 8, 10, 11, 12, 21].
two
Determine how many numbers are in the information set. To do this, simply count each number in the set. Don't forget to count each instance of a repeated value.
- For example, the set [3, three, iv, 5, 7, viii, x, 11, 12, 21] has 10 numbers.
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iii

Prepare up the formula for calculating the upper quartile. The formula is $Q_{iii}={\frac {iii}{four}}(n+1)$ , where $Q_{3}$ is the upper quartile, and $n$ is the number of numbers in the data prepare.^[4]

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2

Complete the adding in parentheses. According to the lodge of operations, you must attend to the parentheses get-go when evaluating a mathematical expression. In this instance, add 1 to the number of numbers in the data fix.
3

Multiply the sum past ${\frac {3}{4}}$ . Yous could also multiply by $.75$ . This will show y'all the placement of the value in the information set that is at the three-fourths, or 75 percent mark, and thus the place where the data set is split into the upper quartile and the lower quartiles. This will not requite y'all the number of the upper quartile.
4
Determine the number representing the upper quartile. If you calculated a whole number, simply find that number in the data set.
- For case, if you calculated 12 using the formula, then the upper quartile is the 12th number in the data set up.
5
Calculate the upper quartile, if necessary. Usually, y'all will calculate a fraction or decimal using the formula. In this case, observe the value to a higher place and beneath this position in the data set, and observe their mean, or average. To do this, dissever the sum of the 2 values by 2. This volition give yous the upper quartile of your data ready.
- For instance, if you lot calculated $8{\frac {1}{4}}$ using the formula, then the upper quartile is between the 8th and 9th number in the data prepare. In the set up [3, 3, 4, 5, 7, viii, 10, 11, 12, 21], 11 and 12 are the 8th and ninth number. Calculate ${\frac {11+12}{2}}$ to observe the average:
  ${\frac {11+12}{ii}}$
  $={\frac {23}{2}}$
  $=eleven.five$
  And then, the upper quartile of the information set is 11.v

1
Input your data into Excel. Enter each value into a separate prison cell. Don't forget to include any repeated values. You lot can enter your information in any cells in the spreadsheet.
- For example, you lot might enter the data gear up [3, three, 4, 5, 7, viii, ten, 11, 12, 21] into cells A1 through A10 in the spreadsheet.
2

Enter the quartile role into another cell. The quartile function is =(QUARTILE(AX:AY, Q)), where AX and AY is the data range, and Q is the quartile.^[5] Begin typing this part into Excel, and then when it pops upward in the menu, double-click on it to select.
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Select the cells containing the data. Select the first cell of the data range, then scroll down or across to select all the cells in the range.
4
Enter 3 into the function to announce the upper quartile. Brand certain you include a comma afterwards the information range, and two closing parentheses.
- For instance, if you desire to find the upper quartile of cells A1 through A10, your part will await like this: =(QUARTILE(A1:A10, iii)).
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Show the upper quartile. To do this, striking enter after typing the role into Excel. This volition show yous the actual upper quartile, not the position of the quartile in the data set.

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Question

How do you find the upper and lower quartiles?

Use the methods above to find the upper quartile. To detect the lower quartile using the formula, use Q1 = ane/4(n+ 1), or enter one into the Excel function instead of 3.
Question

How practice I make up one's mind the inter quartile range of data?

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Customs Answer

The IQR can exist calculated by subtracting the lower quartile from the upper.
Question

How do I summate the upper quartile for a large group of numbers?

Same as for a small group of numbers. Or better use script language like Matlab or Python to load the dataset and practise the calculations.

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You may sometimes see a reference to the "interquartile range." This is the range between the lower and upper quartiles, which is calculated by subtracted Quartile 1 from Quartile three.

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Article Summary Ten

Quartiles are numbers used to dissever a ready of information into iv equal parts or quarters. The upper quartile is the pinnacle 25 per centum of numbers in the data set, or the 75th percentile. To calculate the upper quartile, first, arrange the numbers of the information set in ascending order. So, determine how many numbers are in the set. The formula for calculating the upper quartile is Q3 = ¾ (n +i). Q3 is the upper quartile and n is the number of numbers in your data set. For example, if you have 10 numbers in your data set, you would solve Q3 = ¾ (10 + i), then solve ¾ x 11, which would give you eight ¼. If you get a fraction or decimal as your reply, the upper quartile will exist the average of the number below and above in your information set up. For example, if yous calculate 8 ¼ for Q3 and the numbers below and to a higher place in your set are eight and 10, the boilerplate of them is ix. Therefore, 9 is the upper quartile. To learn how to calculate an upper quartile in Excel, read on!

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