what are the minimume, first quartile, median, third quartile, and maximum of the data set? 2 6 12 8 3 9 14 20
2 answers:
Answer:
Given data set is : 2 6 12 8 3 9 14 20
We shall re-arrange the set of numbers in ascending order to get a clear concept:
2 3 6 8 9 12 14 20
1. Minimum: The minimum is the least value of the data set that is 2.
First quartile: The first quartile value is the median for the numbers before the median. 2 3 6 8 the value is
Median: The average of the center two numbers. =8.5
Third quartile: The third quartile is the same as first but take last 4 values, 9 12 14 20 the value is
Maximum: The highest value number in the data set which is 20.
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Answer:
a) No
b) No
c) No
d) No
Step-by-step explanation:
Remember, a set V wit the operations addition and scalar product is a vector space if the following conditions are valid for all u, v, w∈V and for all scalars c and d:
1. u+v∈V
2. u+v=v+u
3. (u+v)+w=u+(v+w).
4. Exist 0∈V such that u+0=u
5. For each u∈V exist −u∈V such that u+(−u)=0.
6. if c is an escalar and u∈V, then cu∈V
7. c(u+v)=cu+cv
8. (c+d)u=cu+du
9. c(du)=(cd)u
10. 1u=u
let's check each of the properties for the respective operations:
Let
Observe that
1. u+v∈V
2. u+v=v+u, because the adittion of reals is conmutative
3. (u+v)+w=u+(v+w). because the adittion of reals is associative
4.
5.
then regardless of the escalar product, the first five properties are met for a), b), c) and d). Now let's verify that properties 6-10 are met.
a)
6.
7.
8.
Since 8 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product
b) 6.
7.
8.
9.
10
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product
c) Observe that
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product .
d) Observe that
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product .