What measure of spread is used when your data distribution is symmetrical?

What measure of spread is used when your data distribution is symmetrical?

When the data distribution is symmetrical, the appropriate measure of spread is standard deviation. The reason is both sides of symmetrical distribution will have same spread.

Symmetrical distribution: Symmetrical distribution is one when both sides of the distribution are identical. The symmetrical distribution is bell shaped and mean, median and mode are equal in symmetrical distribution.

Standard deviation: Standard deviation is the measure of dispersion. It measures the deviation of a set of numbers from its mean. It is defined as the square root of means of the squared deviations from the arithmetic mean

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

i really dont know

step-by-step explanation: