What Is The Iqr Of A Data Set

Quartile Reckoner

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This quartile calculator and interquartile range calculator finds outset quartile Q₁, second quartile Q₂ and third quartile Q₃ of a data set. It also finds median, minimum, maximum, and interquartile range.

Enter data separated by commas or spaces.

You can also copy and paste lines of data from spreadsheets or text documents. Run into all commanded formats in the table below.

Quartiles

Quartiles mark each 25% of a set of data:

The first quartile Q_ane is the 25th percentile
The second quartile Q₂ is the 50th percentile
The third quartile Q₃ is the 75th percentile

The second quartile Q₂ is easy to find. It is the median of whatever data set and it divides an ordered data set up into upper and lower halves.

The commencement quartile Q₁ is the median of the lower one-half non including the value of Q₂. The tertiary quartile Q_three is the median of the upper half not including the value of Q_two.

How to Calculate Quartiles

Lodge your data set from lowest to highest values
Find the median. This is the 2nd quartile Q₂.
At Q_two separate the ordered data prepare into ii halves.
The lower quartile Q₁ is the median of the lower one-half of the data.
The upper quartile Q₃ is the median of the upper one-half of the data.

If the size of the data set is odd, do not include the median when finding the beginning and 3rd quartiles.

If the size of the data set is even, the median is the average of the middle ii values in the data set up. Add those 2 values, and then divide past 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q₂.

How to Find Interquartile Range

The interquartile range IQR is the range in values from the first quartile Q₁ to the third quartile Q₃. Find the IQR by subtracting Q_i from Q_iii.

IQR = Q₃ - Q₁

How to Find the Minimum

The minimum is the smallest value in a sample data set.

Ordering a information set from lowest to highest value, ten_one ≤ x_two ≤ x₃ ≤ ... ≤ x_n , the minimum is the smallest value x_one . The formula for minimum is:

\[ \text{Min} = x_1 = \text{min}(x_i)_{i=i}^{n} \]

How to Find the Maximum

The maximum is the largest value in a sample data set.

Ordering a data set from lowest to highest value, x_ane ≤ x₂ ≤ x_three ≤ ... ≤ ten_n , the maximum is the largest value x_n . The formula for maximum is:

\[ \text{Max} = x_n = \text{max}(x_i)_{i=1}^{n} \]

How to Notice the Range of a Set of Data

The range of a data fix is the difference between the minimum and maximum. To find the range, calculate 10_n minus 10₁.

\[ R = x_n - x_1 \]

Acceptable Data Formats

Cavalcade (New Lines)

42
54
65
47
59
40
53

42, 54, 65, 47, 59, 40, 53

Comma Separated (CSV)

42,
54,
65,
47,
59,
twoscore,
53,

42, 54, 65, 47, 59, 40, 53

Spaces

42 54
65 47
59 40
53

42 54 65 47 59 forty 53

42, 54, 65, 47, 59, 40, 53

Mixed Delimiters

42
54 65,,, 47,,59,
40 53

42, 54, 65, 47, 59, twoscore, 53

References

[one] Wikipedia contributors. "Quartile." Wikipedia, The Free Encyclopedia. Terminal visited ten April, 2020.

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