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a)
To find the
a)
Answer to Problem 4E
Range = 3.3 pounds and IQR = 0.95 pounds.
Explanation of Solution
Given:
Lowest = 4.15 pounds
Highest = 7.45 pounds
First
Third quartile =6.55 pounds
Standard deviation = 0.65 pounds
Formula:
Using formula,
b)
To explain the shape of the distribution.
b)
Answer to Problem 4E
The distribution is right skewed.
Explanation of Solution
Given:
Lowest = 4.15 pounds
Highest = 7.45 pounds
Mean = 6 pounds
First quartile = 5.6 pounds
Median = 6.2 pounds
Third quartile =6.55 pounds
Standard deviation = 0.65 pounds
If the median is less than the mean then the distribution is left skewed. If the median is greater than mean then the distribution is right skewed. If the both equals then it is symmetric.
Here, Median > mean, the distribution is right skewed.
c)
To convert summary statistics in ounces.
c)
Explanation of Solution
Given:
Lowest = 4.15 pounds
Highest = 7.45 pounds
Mean = 6 pounds
First quartile = 5.6 pounds
Median = 6.2 pounds
Third quartile =6.55 pounds
Standard deviation = 0.65 pounds
We need to multiply each of the value by 16. Therefore, summary statistics becomes,
Mean = 96 ounces
First quartile = 89.6 ounces
Median = 99.2 ounces
Third quartile = 104.8 ounces
Standard deviation = 10.4 ounces
Range = 52.8 ounces
IQR = 15.2 ounces
d)
To explain the change in summary statistics when added 30 ounces.
d)
Explanation of Solution
Given:
Mean = 96 ounces
First quartile = 89.6 ounces
Median = 99.2 ounces
Third quartile = 104.8 ounces
Standard deviation = 10.4 ounces
Range = 52.8 ounces
IQR = 15.2 ounces
Only mean, quartiles and median will be increases by 30. Rest of the things will remain unchanged. Therefore, summary statistic is,
Mean = 126 ounces
First quartile = 119.6 ounces
Median = 129.2 ounces
Third quartile = 134.8 ounces
Standard deviation = 10.4 ounces
Range = 52.8 ounces
IQR = 15.2 ounces
e)
To explain which values will not change if something added to the distribution.
e)
Explanation of Solution
Given:
Mean = 96 ounces
First quartile = 89.6 ounces
Median = 99.2 ounces
Third quartile = 104.8 ounces
Standard deviation = 10.4 ounces
Range = 52.8 ounces
IQR = 15.2 ounces
Something adding in the original distribution means creating outlier for original distribution. Therefore, standard deviations and IQR might not change as these things are unaffected by an adding the values.
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