The drink water bottles off a filling machine are sampled regularly to ensure qu
ID: 3156248 • Letter: T
Question
The drink water bottles off a filling machine are sampled regularly to ensure quality. A sample of n = 14 such bottles is selected at random. The weights of the bottles in the sample in ounces are listed in the following.
15.36 15.97 15.85 15.81 15.47 15.09 15.16 15.14 15.83 15.31 15.36 15.78 15.11 15.06
The weights sorted in ascending order are in the following.
15.06 15.09 15.11 15.14 15.16 15.31 15.36 15.36 15.47 15.78 15.81 15.83 15.85 15.97
You may use the following table to do the computations. Some values have been computed. (hint: you may fill in the column of x2 or ( x - x )2 but not necessarily both).
i
xi
xi - x
( x - x )2
X^2i
1
15.36
–0.09
0.0081
235.9296
2
15.97
0.52
0.2704
255.0409
3
15.85
0.40
0.1600
251.2225
4
15.81
0.36
0.1296
249.9561
5
15.47
0.02
0.0004
239.3209
6
15.09
–0.36
0.1296
227.7081
7
15.16
–0.29
0.0841
229.8256
8
15.14
–0.31
0.0961
229.2196
9
15.83
0.38
0.1444
250.5889
10
15.31
–0.14
0.0196
234.3961
11
15.36
12
15.78
13
15.11
14
15.06
Total
1. The median of this sample is (2)
(A) 15.15 (B) 15.14 (C) 15.45 (D) 15.36 (E) none of the above
2. The mean of this sample is (2)
(A) 15.15 (B) 15.14 (C) 15.45 (D) 15.36 (E) none of the above
3. The mode of this sample is (2)
(A) 15.15 (B) 15.14 (C) 15.45 (D) 15.36 (E) none of the above
4. The range of this sample is (2)
(A) 0.91 (B) 0.94 (C) 15.06 (D) 15.97 (E) none of the above
5. The interquartile range for this sample is (5)
(A) 0.91 (B) 0.67 (C) 0.45 (D) 0.13 (E) none of the above
i
xi
xi - x
( x - x )2
X^2i
1
15.36
–0.09
0.0081
235.9296
2
15.97
0.52
0.2704
255.0409
3
15.85
0.40
0.1600
251.2225
4
15.81
0.36
0.1296
249.9561
5
15.47
0.02
0.0004
239.3209
6
15.09
–0.36
0.1296
227.7081
7
15.16
–0.29
0.0841
229.8256
8
15.14
–0.31
0.0961
229.2196
9
15.83
0.38
0.1444
250.5889
10
15.31
–0.14
0.0196
234.3961
11
15.36
12
15.78
13
15.11
14
15.06
Total
Explanation / Answer
The weights sorted in ascending order is
15.06 15.09 15.11 15.14 15.16 15.31 15.36 15.36 15.47 15.78 15.81 15.83 15.85 15.97
A. N=Sample size=14
If there is an odd number of data values then the median will be the value in the middle. If there is an even number of data values themedian is the mean of the two data values in the middle
=(15.36+15.36)/2=15.36
Answer is D.
2. Mean=Sum of all /N=Sum of (15.06 15.09 15.11 15.14 15.16 15.31 15.36 15.36 15.47 15.78 15.81 15.83 15.85 15.97)
=216.3/14=15.45 Answer is C
3. The "mode" is the value that occurs most often which is 15.36 which is occuring twice.
Answer is D
4. Range=highest-lowest=15.97-15.06=0.91 Answer is A
5. The data is even set hence we divide into 2. we find medians of both the sets and subtract them to get interquartile range
Set 1
15.06 15.09 15.11 15.14 15.16 15.31 15.36
Median=15.14
Set 2
15.36 15.47 15.78 15.81 15.83 15.85 15.97
Median=15.81
IQR=15.81-15.14=0.67
Answer is B
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.