Question

PLEASE ANSWER ALL PARTS AND PROVIDE COMPLETE WORK FOR ALL PARTS.

1. An environmentalist studied 15 fish and measured their liver enzyme levels. After 21 days, she measured the total liver enzyme of each fish and obtained the following values. 124 122 122 135 127 119 134 121 120 132 161 a) (5pts) Construct a Stem and Leaf Plot. b) (Spts) Find the mean, median, mode, maximum and minimum.(round to the nearest tenth 0.0) Means Median Mode= Maximum Minimum c) (Spts) Find the Range, 1" quartile, 2nd quartile, 3 quartile, the interquartile range. Range 1" quartile= 24 quartile 34 quartile- Interquartile Range= d) (5pts) Draw a boxplot of the data.

Answer 1

solution:

Given no.of observations (n) = 15

a) A Stem and Leaf Plot: A stem and leaf plot is a table where data is split into two columns.First column called Stem (consists first digit or digits) and second column called leaf (usually consists last digit)

---> Stem and leaf plot for given data is:

  

Stem	Leaf
11	8 9 9
12	0 1 2 2 4 6 7
13	2 4 5
14	1
15
16	1

b) Frequency distribution for given data

Xi	fi	fi*Xi
118	1	118
119	2	238
120	1	120
121	1	121
122	2	244
124	1	124
126	1	126
127	1	127
132	1	132
134	1	134
135	1	135
141	1	141
161	1	161
	$\sum fi$ or N = 15	Σfi και Χί =1921

i) Mean =   / N = 1921 / 15 = 128.1

Σfi και Χί

ii) N/2 th corresponding observation is our median(Ascending order)

N/2 =~ 8 th observation i.e., 124

  $\therefore$ Median = 124

iii) Mode : Most frequently occurred value.Here data is Bimodal

$\therefore$ Modes are 119 , 122

iv) Maximum value = 161

v) Minimum value = 118

c)

i) Range = Maximum value - Minimum value = 161 - 118 = 43

ii) First quartile(Q1) = 25% percentile = N/4 th observation [ceil value]=~ 4th observation = 120

iii) Second quartile (Q2)= 50% percentile = Median = 124

iv) Third quartile (Q3)= 75% percentile = 3N/4 th observation [ceil value]=~ 12 th observation = 134

v) Inter quartile Range (IQR) = Q3-Q1 = 134 - 120 = 14

d) Box plot is a method of graphical ly depicting groups of numerical data through their quartiles.

--->First identify the First , second and third quartiles and draw verticle lines and connect them as a box

---> Identify if there are any outliers exist which are out of range of (Q1-1.5(IQR) , Q3+1.5(IQR) ) - ( 99 , 155)

If there any exist leave them as dot with out connecting to box plot.

Here 161 is a outlier

162.5- 160 157.5 150- 147.5- 145 142.5 140- 137.5 135- 132.5- 130- 127.5 125- 12.5-

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

162.5- 160 157.5 150- 147.5- 145 142.5 140- 137.5 135- 132.5- 130- 127.5 125- 12.5-