When the outliers are removed, how does the mean change?
2 answers:
<span>In statistics, an outlier is an observation point that is distant from other observations.
Given the points
15, 23, 24, 26, 27 and 35
Notice, that the points 15 and 35 are distance from the other points and hence are outliers.
The mean of the observations including the outliers is given by
The mean of the observations without the outliers is given by
Therefore, </span>when <span>the outliers are removed, the mean remains the same.</span>
Given the points
15, 23, 24, 26, 27 and 35
Notice, that the points 15 and 35 are distance from the other points and hence are outliers.
The mean of the observations including the outliers is given by
The mean of the observations without the outliers is given by
Therefore, </span>when <span>the outliers are removed, the mean remains the same.</span>
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Both equations are equivalent, so there are infinitely many solutions.
Answer:
The actual length of the lap = 250 meters
Step-by-step explanation:
∵ The scale factor of the map is 1:1000
∵ The length of the lap on the map is 25 cm
∴
Where x is the actual length of a lap
∴ x = (25 × 1000) ÷ 1 = 25000 cm
∵ 1 meter = 100 centimeter
∴ The actual length of the lap = 25000 ÷ 100 = 250 meters
The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule . The next number would then be fourth power of 7 plus 1, or 2402.
And the harder way: Denote the <em>n</em>-th term in this sequence by , and denote the given sequence by
.
Let denote the <em>n</em>-th term in the sequence of forward differences of
, defined by
for <em>n</em> ≥ 1. That is, is the sequence with
and so on.
Next, let denote the <em>n</em>-th term of the differences of
, i.e. for <em>n</em> ≥ 1,
so that
etc.
Again: let denote the <em>n</em>-th difference of
:
etc.
One more time: let denote the <em>n</em>-th difference of
:
etc.
The fact that these last differences are constant is a good sign that for all <em>n</em> ≥ 1. Assuming this, we would see that
is an arithmetic sequence given recursively by
and we can easily find the explicit rule:
and so on, up to
Use the same strategy to find a closed form for , then for
, and finally
.
and so on, up to
Recall the formula for the sum of consecutive integers:
and so on, up to
Recall the formula for the sum of squares of consecutive integers: