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MODE (Discrete Series): Inspection
(Frequency Array) Method
Wages f
The value ‘300’ has
100 2 highest frequency i.e
200 1 4.
300 4
400 2 Hence Mode = 300
500 1
Range, Interquartile range, and Box Plot
Range, interquartile range, and box plot are essential statistical concepts used to understand the distribution and
variability of data.
Let us understand about the following in detail:
Range
A dataset's range is determined statistically by deducting the smallest value from the largest value. It is a straightforward
measure of variability.
Example
Range of heights of students in a class = 19.3 (max) - 10.8 (min) = 8.5
As ranges only count extreme values, they occasionally may not have a positive impact on variability.
Interquartile Range
The quartile division of a data set yields the interquartile range (IQR), a statistical measure of statistical dispersion.
In more detail, it is the variation between a data set's upper (Q3) and lower (Q1) quartiles. The data must be arranged
from lowest to highest before the IQR can be calculated. After that, the data set's median (Q2) is calculated, and the
lower quartile (Q1) corresponds to the median of the lower half of the data set (i.e., the data points below the median),
while the upper quartile (Q3) corresponds to the median of the upper half of the data set (i.e., the data points above the
median). Lastly, the IQR is determined as the difference between Q3 and Q1.
Example:
Take into account these numbers: 1, 3, 4, 5, 5, 6, 7, 11. The median value for the first half of the data set is Q1. The middle
value is the average of the two middle values, which is Q1 = (3 + 4)/2 or Q1 = 3.5 as the first half of the data set has an even
number of data points. The middle value in the second half of the data set is Q3. The middle value is the average of the two
middle values, which is Q3 = (6 + 7)/2 or Q3 = 6.5 as again the second half of the data set has an even number of values.
The interquartile range (IQR) thus, is equal to Q3 minus Q1, or 6.5 - 3.5, or 3.
Box Plot
A box plot is a form of chart that is frequently used in explanatory data analysis. It is also referred to as a box and whisker
plot. Box plots use the data's quartiles (or percentiles) and averages to visually depict the distribution of numerical data
and skewness.
Box plots display a dataset's minimum score, first (lower) quartile, median, third (upper) quartile, and maximum scores.
Lower Quartile Median Upper Quartile
Q1 Q2 Q3
Min Max
25% 25% 25% 25%
Whisker Whisker
Box
Inter Quartile Range (IQR)
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