Sure, I'd be glad to walk you through the calculations step-by-step.
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### 3.1.1 Calculate the mean mortality rate of the 10 countries listed.
The mean, or average, is calculated by summing all the mortality rates and then dividing by the number of countries.
Given mortality rates: [tex]\(31, 24, 22, 22, 21, 20, 19, 19, 17, 16\)[/tex]
[tex]\[
\text{Mean} = \frac{31 + 24 + 22 + 22 + 21 + 20 + 19 + 19 + 17 + 16}{10} = \frac{211}{10} = 21.1
\][/tex]
So, the mean mortality rate is 21.1 per 1,000 persons.
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### 3.1.2 Determine the median of the mortality rate of the 10 countries.
The median is the middle value in a data set when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.
Ordered mortality rates: [tex]\(16, 17, 19, 19, 20, 21, 22, 22, 24, 31\)[/tex]
The middle values in this ordered list are the 5th and 6th values: [tex]\(20\)[/tex] and [tex]\(21\)[/tex].
[tex]\[
\text{Median} = \frac{20+21}{2} = 20.5
\][/tex]
So, the median mortality rate is 20.5 per 1,000 persons.
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### 3.1.3 What is the modal value for the data shown above?
The mode is the value that appears most frequently in a data set.
Given mortality rates: [tex]\(31, 24, 22, 22, 21, 20, 19, 19, 17, 16\)[/tex]
Here, the value [tex]\(19\)[/tex] appears twice, which is more than any other value.
So, the modal value is 19 per 1,000 persons.
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### 3.1.4 Determine the value of the lower quartile for the given data.
The lower quartile (Q1) is the median of the lower half of the data set. This is the 25th percentile.
For the ordered set [tex]\(16, 17, 19, 19, 20, 21, 22, 22, 24, 31\)[/tex], the lower half is [tex]\(16, 17, 19, 19, 20\)[/tex]. The median of this subset is [tex]\(19\)[/tex].
So, the lower quartile (Q1) is 19 per 1,000 persons.
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### 3.1.5 Determine the value of the upper quartile for the given data.
The upper quartile (Q3) is the median of the upper half of the data set. This is the 75th percentile.
For the ordered set [tex]\(16, 17, 19, 19, 20, 21, 22, 22, 24, 31\)[/tex], the upper half is [tex]\(21, 22, 22, 24, 31\)[/tex]. The median of this subset is [tex]\(22\)[/tex].
So, the upper quartile (Q3) is 22 per 1,000 persons.
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### 3.1.6 Determine the inter-quartile range for the above data.
The inter-quartile range (IQR) is the difference between the upper quartile and the lower quartile.
Given lower quartile (Q1) = 19 and upper quartile (Q3) = 22:
[tex]\[
\text{IQR} = Q3 - Q1 = 22 - 19 = 3
\][/tex]
So, the inter-quartile range is 3 per 1,000 persons.
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### 3.1.7 Calculate the range for the mortality rate between the highest and lowest values.
The range is the difference between the highest and lowest values in the data set.
Given mortality rates: [tex]\(31, 24, 22, 22, 21, 20, 19, 19, 17, 16\)[/tex]
[tex]\[
\text{Range} = \text{Max} - \text{Min} = 31 - 16 = 15
\][/tex]
So, the range of the mortality rates is 15 per 1,000 persons.
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These calculations provide a comprehensive statistical overview of the mortality rates across the 10 African countries listed.
