STA-301 Assignment No 1:-

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STA(301)

-:Assignment No.1:-

 

Question No.1:-

The following data give index numbers of 40 commodities in a certain year. Classify the following marks in a frequency distribution

138	164	150	132	144	125	149	157	146	158	140
147	136	148	152	144	168	126	138	176	163	119
154	165	142	173	142	147	135	153	140	135	161
145	135	142	150	156	145	128

Also give the class boundaries, cumulative frequency and relative frequency for all the classes.

Answer:-

Identify the smallest and largest values in the data set

Smallest value= X₀= 119

Largest value= X_m = 176

Finding range which is defined as the difference between the largest and smallest value.

Range= X_m- X₀=176-119=57

Deciding the number of classes in the frequency distribution.

n=40

Number of classes=√n=√40=6.32=7

Class interval=h=range/no. of class=57/7=8.2=9

Class Number	Lower Class Limit	Upper Class Limit
1	119	127.2
2	119+9=128	127.2+9=136.2
3	127+9=137	136.2+9=145.2
4	135+9=146	144.2+9=154.2
5	143+9=155	152.2+9=163.2
6	151+9=164	160.2+9=162.2
7	159+9=173	168.2+9=181.2

Class Limit	Class Boundaries	Frequency	Relative Frequency	Cumulative Frequency
119-127.2	118.2-127.2	3	3/119=0.025	3
128-136.2	127.2-136.2	6	6/119=0.050	3+6=9
137-145.2	136.2-145.2	11	11/119=0.076	9+11=20
146-154.2	145.2-154.2	10	10/119=0.084	20+10=30
155-163.2	154.2-163.2	5	5/119=0.042	30+5=35
164-172.2	163.2-172.2	3	3/119=0.025	35+3=38
173-181.2	172.2-181.2	2	2/119=0.017	38+2=40
Total		40

Question No.2:-

The following data represent weight measurements in kilogram of forty individuals in a locality. Construct a stem-and-leaf display of these weight measurements.

48	53	49	52	51	63	60	53	64	59	58	47	49	45
79	65	62	60	68	65	73	88	69	83	78	81	86	92
81	77	82	76	75	91	73	92	64	52	75	85

Answer:-

Stem	Leaf
4	8,7,9,5
5	3,2,1,3,9,8,2
6	3,0,4,5,2,0,8,5,9,4
7	9,3,8,7,6,5,3,5
8	8,3,1,6,1,2,5
9	2,1,2