Techniques for summarizing data

Question 1

what are numerical measures?

Answer 1

-central tendency:
—mean, median, mode

-dispersion:

variance, standard deviation, coefficient of variation, interquartile range

-Relative standing: quantiles

Question 2

what does variance and standard deviation measure?

Answer 2

measures the average scatter around the mean

• the greater the spread or dispersion of the data, the larger the range, variance and SD
• the smaller the spread or dispersion of the data, the smaller the range, variance and SD
• if values are all the same (no variation in data), range, variation and SD will be 0

cannot be negative

Question 3

what is the coefficient of variation?

Answer 3

relative measure of variation, that is expressed in terms of a percentage

denoted by symbol :CV

Question 4

formula for coefficient of variation

Answer 4

CV = (S/X̄) x 100%

S= sample standard deviation

X̄= sample mean

Question 5

how to interpret coefficient of variation

Answer 5

compare two or more sets

CV_calories = 36.08%

Cv_sugar= 57.84%

Relative to the mean, amount of sugar is more variable than calories

If only one data set

CVcalories = 36.08%

standard deviation is 36.08% of mean

Question 6

Describe Z score

Answer 6

is useful in identifyig outliers. Values located far away from the mean will have very small (negative) Z score

or very large (positive) Z scores

Question 7

Formula for Z score

Answer 7

Z = (X - X̄) / S

Question 8

when is a Z score considered an outlier?

Answer 8

if it is less than -3 or greater than +3

Question 9

Describe skewness

Answer 9

Measures the extent to which a set of data is not symmetric

Left or negative skewed: Mean < median

Symmetric: Mean = median

Right or positive skew : Mean > median

Question 10

what are quartiles?

Answer 10

quartiles splits data into four parts:

First quartile (25% of values are smaller or equal to Q₁ and 75% are larger or equal to) , second quartile, third quartile and fourth quartile (25% of values are larger or equal to Q₄ and 75% are smaller or equal to)

Question 11

Formula for Q₁

Answer 11

Q₁ = (n+1)/4 ranked value

Question 12

Formula for Q₃

Answer 12

Q₃= 3(n +1) /4 ranked value

Question 13

What is the formula for interquartile range?

Answer 13

Q₃ - Q₁

Question 14

what does interquartile range measure?

Answer 14

interquartile range measures the spread in the middle 50% of the data.(not influence by extreme values)

eg. IR= 44-35 = 9

Interquartile range in the time to get ready is 9. The interval 35 and 44 is referred to as the middle 50

Question 15

what does box plot look like?

Answer 15