Question

Name: aux pobles Show all relevant work for full credit. Ch.3 08/26/2019 Homework #3 - Math 227 Use the following data to answer the questions. 1.) Consider the following murder rates (per 100.000 people) for each state: AL 13.3 AK 12.9 AZ 941 AR 9.1 FL 11. 0 AZ 9.4 GA 14.4 AR 9.1 ICA 11.7 CO 73 CA 11.7 CT 4.2 TDE 6.7 CO 3 MA 3.7 MI 10.6 MN 2.0 MS 20 MO 10.4 MT 4,8 0104 NM 10.2 NE 3.0 4 8 NV 15.5 10 | MV 155 | MH 1,4 | TN 9.4 TX 14.2 UT 3.7 VT VABA WA 4,6 WV 6.8 BWV 6. BWI 2. 5 WY 7.1 Wi 2.5 NJ 4.4 Calculate the following: a. Mean b. Standard Deviation c. Median 4.16=sx 7.966 buro) e. Range. f. Variance d. Mode. (unctant 3.7, 9:4 g. Midrange h. Determine D 15.5+ 1.4 16.2 i. Find the percentile of the state of CA. j. Determine the outliers, if any. GC-1
can someone help with step by step answers to these problems

Answer 1

Sr. no	X	(X - X̄)²
1	1.4	43.12
2	2	35.60
3	2.5	29.88
4	3	24.67
5	3.3	21.78
6	3.7	18.20
7	3.7	18.204
8	4.2	14.188
9	4.4	12.721
10	4.6	11.334
11	4.8	10.028
12	6.7	1.604
13	6.8	1.361
14	7.1	0.751
15	7.3	0.444
16	8.8	0.694
17	9.1	1.284
18	9.4	2.054
19	9.4	2.054
20	10.2	4.988
21	10.4	5.921
22	10.6	6.934
23	11	9.201
24	11.7	13.938
25	12.6	21.468
26	12.9	24.3378
27	13.3	28.4444
28	14.2	38.8544
29	14.4	41.3878
30	15.5	56.7511

	X	(X - X̄)²
total sum	239	502.21
n	30	30

a)mean =    ΣX/n =    239.000   /   30   =   7.9667

b)sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (502.2067/29)   =       4.1614

c)Median=0.5(n+1)th value =    15.5th   value of sorted data
=   8.05  

d)mode= highest frequency data =    3.7 , 9.4

e)range=max-min =    15.5   -   1.4   =   14.1

f) sample variance =    Σ(X - X̄)²/(n-1)=   502.2067   /   29   =   17.317

g) mid range=(max + min)/2= (   15.5   +   1.4   ) /2 =    8.45

h) D6 = 0.6*(n+1)th value = 18.6th value = 9.4

i) percentile of CA = number of values below CA/n = 23/30=0.7667

so, percentile = 76.76th

j) quartile , Q1 = 0.25(n+1)th value=   7.75th   value of sorted data
=   4.075  
      
Quartile , Q3 = 0.75(n+1)th value=   23.25th   value of sorted data
=   11.175  
      
IQR = Q3-Q1 =    7.1  
      
1.5IQR =    10.65  
      
lower bound=Q1-1.5IQR=   -6.58  
      
upper bound=Q3+1.5IQR=   21.83  
      
outlier =values outside lower bound and upper bound      
total outlier below lower bound=   0  
total outlier above upper bound=   0  
total outlier =    0