Question

find 3 numbers that have the MAD= 1 (mean absolute deviation)

Answer #1

The Mean Absolute Deviation (MAD) of a data set is the average distance between each data value and the mean of the data set.

Let a,b,c be 3real numbers. Then their mean is (a+b+c)/3. The mean absolute distance of a from the mean is |a-(a+b+c)/3| = |(2a-b-c)/3|. Similarly, the mean absolute distance of b from the mean is |b-(a+b+c)/3| = |(2b-a-c)/3| and the mean absolute distance of b from the mean is |c-(a+b+c)/3| = |(2c-a-b)/3| . We have to find a,b,c such that |(2a-b-c)/3|+|(2b-a-c)/3|+|(2c-a-b)/3|=1 or,|(2a-b-c)|+ |(2b-a-c)| +|(2c-a-b)| = 3. Now, let a = -1 ,b = 1 and c = 1.5. Then this equation is satisfied. Thus, the 3 required numbers are -1,1 and 1.5.

For a symmetric distribution with mean µ, the mean absolute
deviation is the expected value MAD(X) = E(|X − µ|), of the
absolute difference |X − µ|, which is strictly positive. The mean
absolute deviation for the standard normal distribution is an
integral 1 √ 2π Z ∞ −∞ |x| e −x 2/2 dx = p 2/π = 0.7979....
Part a: Find the MAD of the Bernoulli-1/2 distribution.
Part b: Find the MAD of the binomial distribution Bin(2,
1/2).
Part...

Calculate the mean and the (sample) standard deviation of the
four numbers: 2, 3, 6, 9
1
(a) Two numbers, a and b, are to be added to this set of four
numbers, such that the mean is increased by 1 and the (sample)
standard deviation is increased by 2.5. Find the values of a and
b.
I want to the values of a and b

Find the mean absolute deviation for the following test scores:
75, 85, 90, 100, 95, 70, 85, 90, 80, 100

Consider the following set of numbers: {0.25, 0.26, 0.23, 0.24,
0.21, 0.30, 0.29}. Calculate the following quantities:
(a)the arithmetic mean, (b)the
median, (c)the standard deviation, and
(d)the median absolute deviation (MAD).

1. Calculate the mean and standard deviation for the numbers 1 –
20.
i.e.) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20
Note: The set of numbers will be considered the population.
µ = _______σ = ________
2. With your calculator, randomly generate 5 numbers from the
numbers 1 – 20, 30 times.
Use:[MATH]>>>PRB #5
RandInt(1,20,5)[ENTER]Note: You cannothave the same number
repeated in the group of 5.
For...

Find the mean, deviation from the mean for each data point, the
square of the deviation for each data point, and the standard
deviation of these numbers.
8, 55, 25, 21,14, 21, 26

Find 3 or more industries which have absolute and/or comparative
advantage in Netherlands.

Let f(x) = x 1/2 (3−x). Find the absolute maximum and absolute
minimum values of the f(x) on the interval [1, 3].

let
y= -x^3 + 6x^2 - 5
a. find all critical numbers for f(x).
b. find the absolute extrema on the interval (-1,3).
c. find the absolute extrema on the interval (1,3).

If a and b are positive numbers, find the absolute maximum value
of the function f(x) = (x^b) (2-x)^a on the interval [0,2]. Your
final answer may depend on a and b.

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