Chapter 3 - Analyzing

Question 1

What is the definition for Central Tendency?

Answer 1

Extent to which the values of numbers group around a central value.

Central or typical value for a probability distribution

Question 2

What are the three main categories for central tendencies?

Answer 2

Arithmetic Mean - Average

Median - Middle value with 50% above and 50% below

Mode - most occurring

Question 3

What is the formula for the mean, and what values drastically affect the overall mean?

Answer 3

Mean - average of all the values

Sum of all values / number of values

It is affected by extreme values or outliers

Question 4

What is the formula to calculate the median of an odd number of values?

How do you calculate the median of an even number of values?

Answer 4

Median for Odd = (n + 1) / 2

Median for Even = (n + 1) / 2 then average the two numbers on both sides of the value

Question 5

When given a population with extreme outliers, is it better to calculate central tendency with the mean or the median?

Answer 5

Median

Question 6

What is the definition of a variation of central tendency?

If the average class grade is 80 percent with a large variance, what does that mean?

Answer 6

The amount of scattering away from a central value

This means, although the average grade is 80 percent, the highest and lowest grades are far from 80

Question 7

What are the four different ways you can measure variation?

Answer 7

Range

Sample Variance

Standard Deviation

Coefficient of Variation

Question 8

What is the formula to calculate the Range?

Answer 8

X largest – X smallest

Question 9

What is the formula to calculate the Variance?

Answer 9

S^2 = [(n ∑ (i=1)) (Xi-¯X )^2 ]

/ (n-1)

Question 10

What is the formula to calculate the Standard Deviation?

Answer 10

S = √[(n ∑ (i=1)) (Xi-¯X )^2]

/ (n-1)

Question 11

What is the formula for the Coefficient of Variation?

Answer 11

CV = (S / ¯X) ⋅ 100%

Question 12

What do we use to calculate extreme outliers, and what is the formula?

Answer 12

Z-Score locates extreme outliers

Z = (X-¯X ) / S

x = current data value
x-bar = sample mean
S = sample standard deviation

Question 13

What are the three different skews of a distribution, and what do each have to do with mean and median?

Answer 13

Left-Skew = mean < median - length is longer on the left

Symmetric = mean = median

Right-Skew = mean > median - length is longer on the right