Six data sets are presented, some of them are samples from a normal distribution, and some of them are samples from populations that are not normally distributed. Identify the samples that are not from normally distributed populations.
L1: Drug concentration six hours after administration
L2: Reading scores on standardized test for elementary children
L3: The number of minutes clerical workers took to complete a certain worksheet
L4: The level of impurities in aluminum cans (in percent)
L5: The number of defective items produced during an hour
L6: The weight of trout in ounces
L1 |
L2 |
L3 |
L4 |
L5 |
L6 |
4.7 |
72 |
4.5 |
2.1 |
21 |
9.9 |
3.2 |
77 |
5.8 |
1.3 |
16 |
11.3 |
5.1 |
65 |
3.7 |
2.8 |
10 |
11.4 |
4.7 |
85 |
4.9 |
1.5 |
10 |
9 |
3.0 |
68 |
4.3 |
1.0 |
11 |
10.1 |
3.4 |
83 |
4.7 |
8.2 |
9 |
8.2 |
4.4 |
73 |
5.8 |
1.9 |
13 |
8.9 |
3.5 |
79 |
3.2 |
9.5 |
12 |
9.9 |
4.5 |
72 |
3.0 |
3.2 |
11 |
10.5 |
5.8 |
81 |
5.1 |
1.3 |
29 |
8.6 |
3.7 |
79 |
3.6 |
4.4 |
10 |
7.8 |
4.9 |
91 |
4.3 |
3.8 |
14 |
10.8 |
5.4 |
69 |
3.6 |
2.7 |
27 |
8.4 |
3.6 |
67 |
5.4 |
8.0 |
10 |
9.6 |
4.3 |
82 |
4.7 |
1.9 |
11 |
9.9 |
3.0 |
66 |
3.0 |
4.9 |
11 |
8.4 |
5.1 |
77 |
3.4 |
4.5 |
12 |
9.0 |
4.3 |
66 |
4.3 |
1.5 |
19 |
9.1 |
Look at your histograms. Which histogram(s) shows significant skew?
Drug concentration six hours after administration |
||
Reading scores on standardized test for elementary children |
||
The number of minutes clerical workers took to complete a certain worksheet |
||
The level of impurities in aluminum cans (in percent) |
||
The number of defective items produced in an hour |
||
The weight of trout in ounces |
Here we use skewness to check for normal distribution here.
Skewness involves the symmetry of the distribution. Skewness that is normal involves a perfectly symmetric distribution. A positively skewed distribution has scores clustered to the left, with the tail extending to the right. A negatively skewed distribution has scores clustered to the right, with the tail extending to the left. Skewness is 0 (or near to 0 in practical cases) in a normal distribution, so the farther away from 0, the more non-normal the distribution.
Formula for skewness:
Calculation:
For skewness = 0,
Mean-Mode = 0 Mean = Median;
So, for checking normal distribution Mean should be equal to Median.
L1:
Mean = 4.25
Median = 4.35
Mean - Median = 0.1 , which is nearing ,therefore, Drug concentration six hours after administration are normally distributed.
L2:
Mean = 75.11
Median = 75
Mean -Median= 0.11, which is nearing zero ,therefore, Reading scores on standardized test for elementary children are normally distributed.
L3:
Mean = 4.3
Median = 4.3
Mean Median, therefore the number of minutes clerical workers took to complete a certain worksheet are normally distributed.
L4:
Mean = 3.58
Median = 2.75
Mean Median, and Mean- Median = 0.83 which is not near zero, therefore The level of impurities in aluminum cans (in percent) are not normally distributed.
L5:
Mean = 14.22
Median = 11.5
Mean Median, and Mean- Median = 2.72 which is not near zero, therefore The number of defective items produced in an hour are not normally distributed.
L6:
Mean = 9.48
Median = 9.35
Mean - Median= 0.13, which is again nearing zero, therefore The weight of trout in ounces are normally distributed.
Hope this will help and you like it.
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