Answer:
[tex]58, 68, 68, 68, 74, 74, 76, 77, 78, 79[/tex]
Step-by-step explanation:
Given
[tex]n=10[/tex]
[tex]Mean = 72[/tex]
[tex]Median = 74[/tex]
[tex]Mode = 68[/tex]
[tex]Range = 21[/tex]
Required
The complete dataset
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From the mean, we have:
[tex]Mean = \frac{\sum x}{n}[/tex]
This gives:
[tex]72 = \frac{\sum x}{10}[/tex]
Cross multiply
[tex]\sum x = 72 * 10[/tex]
[tex]\sum x = 720[/tex]
This means that the sum of all elements of the dataset is 720
Next, we test the median
Since n = 10, then:
[tex]Median = \frac{n + 1}{2}[/tex]
[tex]Median = \frac{10 + 1}{2}[/tex]
[tex]Median = \frac{11}{2}[/tex]
[tex]Median = 5.5th[/tex]
This implies that the median is the average of the 5th and 6th item.
So, we have:
[tex]Median = \frac{5th + 6th}{2}[/tex]
Cross multiply
[tex]5th + 6th = 2 * Median[/tex]
[tex]5th + 6th = 2 * 74[/tex]
[tex]5th + 6th = 148[/tex]
This means that the 5th and 6th element add up to 148
Also, we have:
[tex]Mode = 68[/tex]
This means that 68 has to appear at least twice in the dataset
[tex]Range = 21[/tex]
This implies that the difference between the highest and the least is 21.
The dataset that satisfies the above condition is:
[tex]58, 68, 68, 68, 74, 74, 76, 77, 78, 79[/tex]
