Statistical Analysis on Mode ,Mean, Median, Histogram, Frequency polygon, Cumulative Frequency Distribution, Bar Chart & Pie Chart

  

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     Mode ,Mean, Median, Histogram, Frequency polygon, Cumulative Frequency Distribution, Bar Chart & amp; Pie Chart 

Students Name of  B.B.A Department	Student ID	Study Hours(weekly)
Shefat E noor Khaja Sami	01	8
S.M Sharia Mojumder	02	16
MD Shariful Islam	03	24
Romana Islam	04	18
Dilruba Aktar	05	10
Effana Binta Haque	06	5
Youna Azrin Chowdhury	07	4
Sharf Shihab Hussain	08	10
Tanjila Zaman	09	30
K.M Sadman Sakib	10	25
Asif Hasan Mahmud	11	8
MD Asfaq Hossain	12	3
Shariar Chowdhury	13	9
Asif-Ul-Kabir	14	8
Md. Yousuf Mozumder	15	12
MD Alamgir hossain Khan	16	17
Nabid Ahmed	17	27
Sujan Chandra Sarkar	18	20
Shampa Saha	19	12
Md. Mehedi Hasan	20	21
Students Name Of English Department	Student ID	Study Hours(weekly)
Md Shahin Uddin	21	8
Mohiyan Haque	22	10
Nigan Sultana	23	4
Nasrin Saiba Dipa	24	15
Tazma Islam	25	28
Maisha Tabassum	26	21
Asma Aktar	27	3
Rebad Ahamed	28	35
A.H.M Rezwanul Haque	29	20
Sonia Akter	30	40
Miftahul Jannat Luna	31	7
Irin Zaman	32	11
Rabeya Khatun	33	17
Afnaza Khanom Zuna	34	5
jannatul Ferdush Rasha	35	23
Jnanee Oman Khaiyam	36	9
Sorwar Uddin	37	16
Mayaniz Khanam Shimul	38	9
Kamrun Nahar Dola	39	5
ShaikaTasnim Khan	40	10
Students Name of Economics Department	Student ID	Study Hours(weekly)
Amzad Hossain	41	8
Surid Saeed	42	15
Ashraf Ahmed	43	18
Md. Saiful Islam	44	24
Shafayet Hossain	45	7
Towhid Hasan Tamal	46	10
Md. Farhad Hossain	47	24
Mir Kamaruzzaman	48	16
Dowla Biswas	49	21
Syeda Raisa Tazneen	50	28
Tasnim Shaba Mostafa	51	30
Nourin Rahman	52	25
Tanzina Sharmin Toma	53	26
Kashfia Hossain	54	21
Ahmed Shatil	55	6
Md. Mahfuzul Hasan	56	15
Mariha Sabah	57	7
Md. Ashikuzzaman Shoshee	58	18
Md. Imran Hossain	59	20
Md. Abu Nayem Shawon	60	25
Students name of ECE Department	Student ID	Study Hours(weekly)
Md. Forhad Shamim	61	18
Md. Talha	62	15
Nausiba Nahin	63	9
Md. Muzahedul Hoque	64	7
Md. Saidur Rahman	65	5
Hasanuzzaman Sayem	66	16
Afsana Umme Hani	67	12
Istiaq Ahmed Shovon	68	14
Sahanur Rahman Shohag	69	12
Md. Naimul Islam	70	10
Mahinul Mannan	71	24
Sajjad Hossain	72	28
Pritom Roy	73	8
Kazi Ashrafuzzaman	74	16
Inzamamul Hossain	75	20
Pappu Talukder	76	15
Saaif Mahamud	77	6
Md.Faizur Rahman	78	7
Md. Sabuj Miah	79	12
Md. Anisur Rahman	80	10

There are sample of 80 students weekly study hours.

8, 16, 24, 18, 10, 5, 4, 10, 30, 25, 8, 3, 9, 8, 12, 17, 27,  20, 12, 21, 8, 10, 4, 15, 28, 21, 3, 35, 20, 32, 7, 11, 17, 5, 23, 9, 16, 9, 5, 10, 8, 15, 18, 24, 7, 10, 24, 16, 21, 28, 30, 25, 26, 21, 6, 15, 7, 18, 20, 25 ,18, 15, 9, 7, 5,  16, 12, 14,  12, 10, 24, 28 , 8, 16, 20, 15, 6, 7, 12, 10.

There are total number of observation is 80. So n=80

Number of Class:

We know that No. of class = 2^k > n. So here k = 7

Class Interval:

We know that, i  ≥ H-L/k   35-3/7 = 4.57. So i = 5

Ø  Organize the data into a frequency table :

Table-1

class interval	frequency	Relative frequency	Class midpoint	Cumulative frequency	Upper Limit
1 to 6	8	0.1	3.5	8	6
6 to 11	24	0.3	8.5	32	11
11 to 16	12	0.15	13.5	44	16
16 to 21	15	0.1875	18.5	59	21
21 to 26	12	0.15	23.5	71	26
26 to 31	7	0.0875	28.5	78	31
31 to 36	2	0.025	33.5	80	36

Fig: 01

Now we draw a histogram from the table-1. In this diagram, the horizontal axis contains the value of class midpoint and the vertical axis contains the value of frequency. From the above histogram we can say that the class midpoint 8.5 contains the highest frequency that is 24. And class midpoint 33.5 shows the lowest frequency is 2.

Fig:2

Now we draw a frequency polygon from the table-1. In this figure, the horizontal axis contains the value of class midpoint and the vertical axis contains the value of frequency. From the above frequency polygon we can say that the class midpoint 8.5 shows the highest frequency that is 24. And class midpoint 33.5 shows the lowest frequency is 2

Fig: 3

Now we draw a cumulative frequency distribution from the table-1. In this figure, the horizontal axis contains the value of upper class limit and the vertical axis contains the value of cumulative frequency. At first, the curve is dramatically increased and then slowly increased. So we can say that the curve is increasing curve.

Ø  Calculating Mean, Median  and mode:

Mode:

Here most repeated value is 10 in our total number of observation. So for ungroup data the mode is 10 hours per week

We draw a table for calculating mean and median for group data.

Table – 2:

­­­­­­class interval	­­­­­­­Frequency(f)­­­­	Class midpoint(x)	fx	Cumulative frequency
1 to 6	8	3.5	28	8
6 to 11	24	8.5	204	32
11 to 16	12	13.5	162	44
16 to 21	15	18.5	277.5	59
21 to 26	12	23.5	282	71
26 to 31	7	28.5	199.5	78
31 to 36	2	33.5	67	80
	80		∑fx=1220

Mean for group data:

X = ∑fx /n

=1220/80

=15.25

Median for group data:

M_e

Here, n=80, so 80/2 = 40, i.e in the table the median class is (6 up to 111). From the table

L=11, n=80, f=12, i=5, CF=32

M_e

       = 14.33

                                                                                                                             

Here, mean > median > mode, so the distribution is positively skewed.

Here shows weekly study hours on the basis of the departments:

Fig: 4

Now we draw a Bar Diagram from the table-2. In this Diagram, the horizontal axis contains the name of four departments and the vertical axis contains the value of average study hours. Here the students of Economics department show the highest study hours. And the other departments study hours almost same.

Here shows weekly study hours in a bar chart on the basis of the class limit:

Fig: 5

Now we draw a Bar chart from the table-2. In this diagram, the horizontal axis contains the value of class interval and the vertical axis contains the value of frequency. From the above Bar chart we can say that the class interval 6 to 11 shows the highest frequency that is 24. And class interval 31 to 36 shows the lowest frequency is 2.

Here shows the Bar Chart on the basis of total observation in percentage.

Fig: 6

Now we draw a Bar Diagram from the table-2. In this Diagram, the horizontal axis contains the name of four departments and the vertical axis contains the value of average study hours. Here the students of Economics department show the highest study hours. And the other departments study hours almost same.

Here shows weekly study hours in a pie diagram on the basis of the class limit:

Fig: 7

Now we draw a Pie Chart from the table-2. The pie chart shows the highest percentage of study hours that is 30% in the class limit of 6 to 11.

Fig: 8

Now we draw a Pie Chart from the table-2. Here the students of Economics department show the highest percentage of study hours. And the other departments study hours percentage almost same.

Thankyou