Question

The data in the accompanying table represent the length of life, in years, measured to the nearest tenth, of 30 similar fuel pumps. Complete parts (a) through (c) below.

(a) Construct a stem-and-leaf plot for the life in years of the fuel pumps, using the digit to the left of the decimal point as the stem for each observation.

(b) Set up a relative frequency distribution.

(c) Compute the sample mean, sample range , and sample standard deviation.

2.6 3.5 0.4 3.3 1.3 0.2

0.2 5.5 5.1 6.7 0.6 2.4

1.6 3.7 5.5 1.8 4.9 0.4

4.4 0.8 1.5 0.5 2.3 5.1

0.9 5.6 5.7 6.2 1.2 0.4

Answer 1

a)

stem	leaf
0	2,2,4,4,4,5,6,8,9
1	2,3,5,6,8
2	3,4,6
3	3,5,7
4	4,9
5	1,1,5,5,6,7
6	2,7

b)

class interval	frequency	relative frequency=fi/N
0.2-1.2	10	10/30=0.33
2.2-3.2	7	7/30
4.2-5.2	7	7/30
6.2-7.2	6	6/30=0.2

c)

Sr. no	X	(X - X̄)²
1	2.6	0.044
2	0.2	6.812
3	1.6	1.464
4	4.4	2.528
5	0.9	3.648
6	3.5	0.476
7	5.5	7.236
8	3.7	0.792
9	0.8	4.040
10	5.6	7.784
11	0.4	5.808
12	5.1	5.244
13	5.5	7.236
14	1.5	1.716
15	5.7	8.352
16	3.3	0.240
17	6.7	15.132
18	1.8	1.020
19	0.5	5.336
20	6.2	11.492
21	1.3	2.280
22	0.6	4.884
23	4.9	4.368
24	2.3	0.260
25	1.2	2.592
26	0.2	6.812
27	2.4	0.168
28	0.4	5.808
29	5.1	5.244
30	0.4	5.808

	X	(X - X̄)²
total sum	84.3	134.627
n	30	30

mean =    ΣX/n =    2.81
      
sample variance =    Σ(X - X̄)²/(n-1)=   4.642
      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   2.1546

maximum =    6.7
minimum=   0.2
  
range=max-min =    6.5