Question

The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest. 16; 17; 19; 20; 20; 21; 22; 23; 24; 24; 24; 25; 25; 26; 26; 26; 27; 28; 29; 32; 33; 33; 34; 35; 37; 39; 40

g. What percent of people surveyed visited a store at least 3 times?

h. Find the 40th percentile.

i. Construct a histogram of the data.

j. Find the percentile of data point 29.

k. State whether the data are symmetrical, skewed to the left, or skewed to the right.

l. Find the sample standard deviation.

Answer 1

g) total people surveyed visited a store at least 3 times=6

percentage = 6/27 =22.22%

h) 40th percentile = 0.40(n+1)th value = 11.2th value of sorted data = 148

i)

class interval	frequency
16-20	5
21-25	8
26-30	6
31-35	5
36-40	3

Histogram

j)

percentile of 29=total data points above 29/total data poitns*100=18/27*100=66.67

k)

data is slightly skewed to right

l)

X	(X - X̄)²
16	117.763
17	97.059
19	61.652
20	46.948
20	46.948
21	34.244
22	23.540
23	14.837
24	8.133
24	8.133
24	8.133
25	3.429
25	3.429
26	0.726
26	0.726
26	0.726
27	0.022
28	1.318
29	4.615
32	26.503
33	37.800
33	37.800
34	51.096
35	66.392
37	102.985
39	147.578
40	172.874

	X	(X - X̄)²
total sum	725	1125.407407
n	27	27

mean =    ΣX/n =    26.85
      
  
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   6.58