PLEASE HELP ME TO GET THE HISTOGRAM, FREQUENCY POLYGON AND PIE CHART OF THE PICTURE BELOW.
PLEASE HELP ME TO GET THE HISTOGRAM, FREQUENCY
THE SOLUTION WAS PROVIDED BELOW:
The mean gives the average of all the observation and it calculated for grouped frequency table as :
x¯=∑fx∑f
The median is the middle value of the data set and it calculated for grouped frequency table as :
Md=l+n2-cf×h
where n is the number of observation, l is the lowest boundary and f is the frequency and h is the class width.
Mo=l+f-f12f-f1-f2×h
The data given for 40 students based on the 25 point test and it is defined as :
Scores | Class boundary | f | x | fx | fxi-x¯2 | Cumulative frequency |
5-7 | 4.5-7.5 | 2 | 6 | 12 | 136.125 | 2 |
8-10 | 7.5-10.5 | 4 | 9 | 36 | 110.25 | 6 |
11-13 | 10.5-13.5 | 14 | 12 | 168 | 70.875 | 20 |
14-16 | 13.5-16.5 | 9 | 15 | 135 | 5.0625 | 29 |
17-19 | 16.5-19.5 | 6 | 18 | 108 | 84.375 | 35 |
20-22 | 19.5-22.5 | 3 | 21 | 63 | 135.6875 | 38 |
23-25 | 22.5-25.5 | 2 | 24 | 48 | 190.125 | 40 |
Total | 40 | 570 | 733.5 |
From the information given :
Percentile 20 :
Let, 20×n100=20×40100=8
The cumulative frequency greater than 8 is 20 and its corresponding frequency and lower boundary as 14 and 10.5 respectively. The class width is 3 and the cumulative value is 6.
Now,
P20=l+20n100-cf×h=10.5+8-614×3=10.5+0.429=10.929
Thus, P20=10.929
Decile 2 :
Let, 2×n10=2×4010=8
The cumulative frequency greater than 8 is 20 and its corresponding frequency and lower boundary as 14 and 10.5 respectively. The class width is 3 and the cumulative value is 6.
Now,
D2=l+2n10-cf×h=10.5+8-614×3=10.5+0.429=10.929
Thus, D2=10.929
Let, 2×n4=2×404=20
The cumulative frequency greater than 20 is 29 and its corresponding frequency and lower boundary as 9 and 13.5 respectively. The class width is 3 and the cumulative value is 20.
Now,
Q2=l+2n4-cf×h=13.5+20-209×3=13.5+0=13.5
Thus, Q2=13.5
Using the table values :
Mean :
x¯=∑fx∑f=57040=14.25
Mean is 14.25
Median :
Let, n2=402=20
The cumulative frequency greater than 20 is 29 and its corresponding frequency and lower boundary as 9 and 13.5 respectively. The class width is 3 and the cumulative value is 20.
Now,
Md=l+n2-cf×h=13.5+20-209×3=13.5+0=13.5
Thus, Md=13.5
Mode :
Using the data given, highest frequency is 14 and its corresponding lower boundary as 10.5. The upper and lower frequency of highest frequency is 4 and 9 respectively. The class width is 3 .
Now,
Mo=l+f-f12f-f1-f2×h=10.5+14-42×14-4-9×3=10.5+2=12.5
Thus, Mo=12.5
![Example: Grouped Data
Compute the variance and standard deviation of the following grade
distribution of 40 students based on their 25-point test.
Step 2.
fx
f(x – x)²
Scores
f
Solve for Variance
|
5-7
2
6
12
136.1250
Ef(x-x)2
n - 1
s2
8-10
4
9.
36
110.2500
733.5
11-13
14
12
168
70.8750
s2
40 – 1
14-16
15
135
5.0625
s2
18.8077
%3D
17-19
18
108
84.3750
Step 3.
20-22
3
21
63
135.6875
Solve for Standard
Deviation
23-25
2
24
48
190.125
s = 4.34
n=40
570
733.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18381f78-cb47-43a8-9f59-9e2d4fcdbfcc%2Fda32cb36-3a8c-4b12-be6b-8cebcbdae889%2Fli4civ_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 2 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)