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taehyungg
14.01.2021 •
Mathematics
Find the mean and compare it with the median. Find the standard deviation and compare it with the interquartile range
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Ответ:
Question:
Find the mean and compare it with the median. Find the standard deviation and compare it with the interquartile range. Calculate s for the data 4, 1, 3, 10, 2.
(a)
(b)
Step-by-step explanation:
Given:
Data: 4, 1, 3, 10, 2.
Solving (a): The mean and the Median
The mean is calculated as follows:
Where
So, the expression becomes:
Calculating the Median:
First, arrange the order (ascending order):
Because n is odd
The median is represented as:
From the arranged data, the 3rd item is 3.
Hence:
By comparison, the mean is greater than the median because![4 3](/tpl/images/1035/4044/aae98.png)
Solving (b): Standard Deviation and IQR
The standard deviation is calculated as follows:
So, we have:
Calculating IQR
In (a), we calculate the median as:
First, we calculate![Q_1](/tpl/images/1035/4044/0d6d0.png)
The first half is:
So:
First, we calculate![Q_3](/tpl/images/1035/4044/c8814.png)
So:
Recall that:
So, we have:
By comparison, the standard deviation is greater than the IQR because:
So,
Ответ:
Time. Water
0.5. 0.8
1. 1.6
3. 4.8
25. 40