Concept explainers
a.
Find the
a.
Answer to Problem 63E
The mean of the data set is 4.8.
Explanation of Solution
Calculation:
If
Mean:
If
The mean value is calculated as,
Substitute the values in the above formula,
Hence, the mean of the data set is 4.8.
b.
Prepare one table like the Table 3.5 in the book with an additional column of
b.
Answer to Problem 63E
The table is given below:
x | |||
1 | –3.8 | 3.8 | |
3 | –1.8 | 1.8 | |
4 | –0.8 | 0.8 | |
7 | 2.2 | 2.2 | |
9 | 4.2 | 4.2 | |
Total | 0 | 40.8 | 12.8 |
Explanation of Solution
Calculation:
The Table 3.5 consists of
x | |||
1 | –3.8 | 3.8 | |
3 | –1.8 | 1.8 | |
4 | –0.8 | 0.8 | |
7 | 2.2 | 2.2 | |
9 | 4.2 | 4.2 | |
Total | 0 | 40.8 | 12.8 |
c.
Find SD and MAD from the table.
c.
Answer to Problem 63E
The SD and the MD are 3.1937 and 2.56 respectively.
Explanation of Solution
Calculation:
Standard deviation:
Let
The sample standard deviation can be expressed as,
The table from part (a), is,
x | |||
1 | –3.8 | 3.8 | |
3 | –1.8 | 1.8 | |
4 | –0.8 | 0.8 | |
7 | 2.2 | 2.2 | |
9 | 4.2 | 4.2 | |
Total | 0 | 40.8 | 12.8 |
Substitute the value in the above formula,
Substitute the values in the MD formula,
Hence, the SD and the MD are 3.1937 and 2.56 respectively.
d.
Find SD and MAD for the new data set.
d.
Answer to Problem 63E
The SD and the MD are 10.677 and 7 respectively.
Explanation of Solution
Calculation:
The data values are 1, 3, 4, 7, 9, and 30.
Substitute the values in the mean formula,
The table of
x | |||
1 | –8 | 64 | 8 |
3 | –6 | 36 | 6 |
4 | –5 | 25 | 5 |
7 | –2 | 4 | 2 |
9 | 0 | 0 | 0 |
30 | 21 | 441 | 21 |
Total | 0 | 570 | 42 |
Substitute the value in the above formula,
Substitute the values in the MD formula,
Hence, the SD and the MD are 10.677 and 7 respectively.
e.
Identify the resistant measure between standard deviation and mean deviation about mean.
e.
Answer to Problem 63E
The mean deviation about mean is more resistant than standard deviation.
Explanation of Solution
From part (c), the SD and the MD are 3.1937 and 2.56 respectively.
From part (d), the SD and the MD for new data are 10.677 and 7 respectively.
Hence, after adding the outlier value, the mean deviation about mean has changed less comparative to standard deviation.
Hence, it can be said that the mean deviation about mean is more resistant than standard deviation.
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Chapter 3 Solutions
ESSENTIAL STATISTICS W/CONNECT
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill