To draw the box and whisker plot, we have to follow the instruction given below.
Step 1 :
Arrange the data from least to greatest
Step 2 :
Calculate the median(Q_{2}) which divides the data into two equal parts.
Step 3 :
Step 4 :
Problem 1 :
Draw a box and whisker plot for the data set:
12, 14, 14, 12, 16, 13, 11, 14, 18
Solution:
Let us write the observations in the data in ascending order.
11, 12, 12, 13, 14, 14, 14, 16, 18
Median is dividing the data set into two parts.
Lower quartile Q_{1}:
The data set is having four values. So,
Q_{1} = (12 + 12) / 2
= 24/2
Q_{1 }= 12
Upper quartile Q_{3}:
The data set is having four values. So,
Q_{3} = (14 + 16) / 2
= 30/2
Q_{3 }= 15
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 14
Problem 2 :
Draw a box and whisker plot for the data set:
16, 14, 13, 13, 18, 12, 11, 12, 12
Solution :
Let us write the observations in the data in ascending order.
11, 12, 12, 12, 13, 13, 14, 16, 18
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (12 + 12) / 2
= 24/2
Q_{1 }= 12
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (14 + 16) / 2
= 30/2
Q_{3 }= 15
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 13
Problem 3:
Draw a box and whisker plot for the data set:
32, 34, 36, 37, 36, 37, 38, 37, 38
Solution :
Let us write the observations in the data in ascending order.
32, 34, 36, 36, 37, 37, 37, 38, 38
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (34 + 36) / 2
= 70/2
Q_{1 }= 35
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (37 + 38) / 2
= 75/2
Q_{3 }= 37.5
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 37
Problem 4 :
Draw a box and whisker plot for the data set:
22, 24, 25, 26, 21, 22, 28, 29, 23
Solution :
Let us write the observations in the data in ascending order.
21, 22, 22, 23, 24, 25, 26, 28, 29
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (22 + 22) / 2
= 44/2
Q_{1 }= 22
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (26 + 28) / 2
= 54/2
Q_{3 }= 27
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 24
Problem 5 :
Draw a box and whisker plot for the data set:
52, 52, 55, 55, 53, 56, 57, 57, 58
Solution :
Let us write the observations in the data in ascending order.
52, 52, 53, 55, 55, 56, 57, 57, 58
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (52 + 53) / 2
= 105/2
Q_{1 }= 52.5
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (57 + 57) / 2
= 114/2
Q_{3 }= 57
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 55
Problem 6 :
Draw a box and whisker plot for the data set:
34, 38, 34, 37, 32, 32, 39, 34, 39
Solution :
Let us write the observations in the data in ascending order.
32, 32, 34, 34, 34, 37, 38, 39, 39
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (32 + 34) / 2
= 66/2
Q_{1 }= 33
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (38 + 39) / 2
= 77/2
Q_{3 }= 38.5
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 34
Problem 7 :
Draw a box and whisker plot for the data set:
50, 51, 52, 58, 58, 59, 49, 50, 49
Solution :
Let us write the observations in the data in ascending order.
49, 49, 50, 50, 51, 52, 58, 58, 59
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (49 + 50) / 2
= 99/2
Q_{1 }= 49.5
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (58 + 58) / 2
= 116/2
Q_{3 }= 58
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 51
Problem 8 :
Draw a box and whisker plot for the data set:
37, 38, 36, 33, 34, 32, 34, 37, 32
Solution :
Let us write the observations in the data in ascending order.
32, 32, 33, 34, 34, 36, 37, 37, 38
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (32 + 33) / 2
= 65/2
Q_{1 }= 32.5
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (37 + 37) / 2
= 74/2
Q_{3 }= 37
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 34
Problem 9 :
Draw a box and whisker plot for the data set:
18, 16, 15, 19, 11, 14, 12, 14, 16
Solution :
Let us write the observations in the data in ascending order.
11, 12, 14, 14, 15, 16, 16, 18, 19
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (12 + 14) / 2
= 26/2
Q_{1 }= 13
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (16 + 18) / 2
= 34/2
Q_{3 }= 17
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 15
Problem 10 :
Draw a box and whisker plot for the data set:
55, 56, 58, 59, 54, 54, 51, 53, 52
Solution :
Let us write the observations in the data in ascending order.
51, 52, 53, 54, 54, 55, 56, 58, 59
Median is dividing the data set into two parts.
Median of lower half Q_{1}:
The data set is having four values. So,
Q_{1} = (52 + 53) / 2
= 105/2
Q_{1 }= 52.5
Median of upper half Q_{3}:
The data set is having four values. So,
Q_{3} = (56 + 58) / 2
= 114/2
Q_{3 }= 57
Median Q_{2}:
The median is the middle value in a set of data.
So, median Q_{2 }= 54
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