3.1

Question 1

symmetric distributions

Answer 1

shows mirror symmetry about the centre

Question 2

uniform distribution

Answer 2

each outcome has a similar frequency, each outcome appears equally likely to occur, distribution is symmetric, no mode, median/mean in the middle

Question 3

mound shaped distribution (normal, bell, gaussian)

Answer 3

each outcome has a decreasing frequency from the middle or interval with the greatest frequency, distribution is symmetric, median mean mode all in middle

Question 4

u shaped distribution

Answer 4

frequencies are greater at the end intervals (bimodal) distribution is symmetric, a bimodal distribution may suggest another population group within the larger group, median/mean in middle, mode at the ends

Question 5

skewed distribution

Answer 5

asymmetrical distribution where the direction denotes skew type, right skewed has a tail to the right, left skewed has a tail to the left, mode doesn’t have have to be on the opposite tail

Question 6

right skewed

Answer 6

mode at peak, mode then median then mean, tail to the right, x̅ > med

Question 7

left skewed

Answer 7

mode at peak, mean then median then mode, tail to the left, x̅ < med

Question 8

pearsons index of skewness

Answer 8

PI = [3(x̅ - median)]/s

Question 9

sample stdev

Answer 9

s = √(∑(x-x̅)^2)/n-1

Question 10

if |PI| ≥ 1

Answer 10

then the data is significantly skewed

Question 11

if PI ≥ 1

Answer 11

then the data is right skewed

Question 12

if PI ≤ - 1

Answer 12

then the data is left skewed

Question 13

PI ≈ 0

Answer 13

means x̅ ≈ med, symmetric, not normal recess, could be uniform, mound, u-shaped

Question 14

outlier

Answer 14

data value is considered an outlier if the value is 1.5(IQR) below Q1 or 1.5(IQR) above Q3

Question 15

IQR

Answer 15

interquartile range, the difference between Q3 and Q1

Question 16

reason for outliers

Answer 16

valid data obtained by chance, mistake in data process (measurement or observation error), sample size not large enough, improper sampling (incorrect population), recording error/transposition error

Question 17

outlier for normal distribution

Answer 17

outlier if it’s 3 or more stdev away from the x̅