A box plot can be used to graphically represent the data set.

**Box
plot**

A box plot can be used to graphically represent the data set. These
plots involve five specific value.

(i)
The lowest value of the data set (i.e., minimum), (ii) Q_{1} (iii) The
median (iv) Q_{3} , (v) The highest value of the data set (i.e maximum)

These value are called a five-number summary of the data set.

A box plot is a graph of a data
set obtained by drawing a horizontal line from the minimum data value to
Q_{1} and a horizontal line from Q_{3 }to the maximum data
value, and drawing a box by vertical lines passing through Q_{1} and Q_{3},
with a vertical line inside the box passing through the median or Q_{2}.

1.
If the median is near the center of the box, the distribution is
approximately symmetric

2.
If the median falls to the left of the center of the box, the
distribution is positively skewed.

3.
If the median falls to the right of the center of the box, the
distribution is negatively skewed.

4.
If the lines are about the same length, the distribution is
approximately symmetric

5.
If the right line is larger than the left line. the distribution
is positively skewed.

6.
If the left line is larger than the right line. the distribution
is negatively skewed.

**Remark:**

(i) The line drawn from minimum value of the dataset to Q1 and Q3 to the maximum value of the data set is called whisker.

(ii) Box plot is also called Box – Whisker plot.

(iii) A box and whisker plot illustrate the spread of the distribution and also gives an idea of the shape of the distribution

The following data gives the Number of students studying in XI
standard in 10 different schools 89,47,164,296,30,215,138,78,48,39 construct a
boxplot for the data.

**Step 1 : **Arrange the data in order

30,39,47,48,78,89,138,164,215,296

**Step 2 :** Find the median

**Step 5 :** Find
the minimum and maximum values.

**Step 6 :** Locate
the lowest value, Q_{1}, median, Q_{3} and the highest value on
the scale.

**Step 7 :** Draw a
box through Q_{1} and Q_{3}

Construct a box –whisker plot for the following data

96, 151, 167, 185, 200, 220, 246, 269, 238, 252, 297, 105, 123,
178, 202

**Step 1 :** Arrange
the data in code

96,105,123,151,167,178,185,200,202,220,238,246,252,269,297.

**Step 2 :** Find
the Median

8th term Median = 200

**Step 3 :** Find Q_{1}
(middle of previous terms of 200)

96,105,123,151,167,178,185

Q_{1} =151

**Step 4 :** Find Q_{3}
(middle of successive terms of 200)

202,220,238,246,252,269,297

Q_{3} =246

**Step 5 :** Minimum
value = 96, Maximum Value = 297

**Step 6 :** Draw a
scale for the data on the x axis

**Step 7:** Locate the five
numbers in the scale and draw a box around

Tags : Statistics , 11th Statistics : Chapter 6 : Measures of Dispersion

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11th Statistics : Chapter 6 : Measures of Dispersion : Box plot | Statistics

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