1.3 and 1.4 Overview and Descriptive Stats

Question 1

Smoothed histogram

Answer 1

Density estimate

Question 2

Sample Statistics

Answer 2

Numbers describing a sample distribution

• measures of CENTER (mean, median)
• measures of spread (standard deviation, range, IQR)
• other: min, max, quartiles

Question 3

sample mean

Answer 3

x bar

Question 4

population mean

Answer 4

impossible to find bc you can’t get data from everyone ever

dealt with theoretically with infinite populations

Question 5

drawback of the Mean

Answer 5

sensitive to outliers

-if the data is not symmetric, the mean isn’t very good at measuring the center

Question 6

median

Answer 6

~x
middle value
outliers DO NOT change the median = resistant

Question 7

median when n is odd vs even

Answer 7

odd, after ordering, median = (n+1)/2 th data value

even, after ordering, median = avg of n/2 th and (n/2 + 1)th data values

Question 8

using population mean and population median

Answer 8

1. symmetric distribution: u = ~u
(mean & median are close together)
2. negatively skewed distribution u < ~u
3. positively skewed distribution u > ~u
mean gets pulled towards median and vice versa

Question 9

Quartiles

Answer 9

Q1: median of data values < ~x (25%)
Q3: median of data values > ~x (75%)
range = max - min

Question 10

Boxplot

Answer 10

visual representation of 5 number summary (max, min, median, Q1, Q3)

Question 11

Interquartile Range (IQR)

Answer 11

range of middle 50% of data

IQR = Q3 - Q1

Question 12

How to identify outliers

Answer 12

• find IQR
• multiply * 1.5 (1.5 IQR rule)
• subtract that # from Q1 and then from Q3
• anything above #-Q3 and below #-Q1 = outlier

Question 13

Deviation from mean

Answer 13

xi - x bar

Question 14

summation of (xi-x bar) =

Answer 14

0, always

bc…

Question 15

sample variance s^2

Answer 15

= summation of (xi-x bar)^2
/(n-1)
*if you know the mean and the n-1 values, then you know the last value

Question 16

n-1

Answer 16

degrees of freedom

since summation of (xi-x bar) = 0, the last deviation can always be calculated if first n-1 is known

Question 17

Sample Standard Deviation

Answer 17

how spread out the data is
(only really good with symmetric data)
s = sqrt(s^2)
NOT resistant to outliers

Question 18

When to use standard deviation (s) vs IQR as measure of spread***

Answer 18

• measure of center = mean, use (s)

- measure of center = median, use IQR

Question 19

Finite population standard deviation

Answer 19

sigma o-bar

sqrt(summantion (xi-x bar)^2 / N)

Question 20

Letters rule of thumb

Answer 20

roman = sample
greek = population (parameters)
mew (u) = mean pop
x bar = mean sample
sigma (o bar) = standard deviation pop
s = standard deviation sample

Question 21

Standard deviation and the mean tell if your data is

Answer 21

centered, symmetric, or dispersed

Question 22

Bell shaped data =

Answer 22

normally distributed

Question 23

Empirical Rule

Answer 23

68-95-99.7% rule
1 standard deviation = 68% of data
2 standard deviations = 95% data
3 standard deviations = 99.7% data

Question 24

Z-score

Answer 24

• standard deviation = ruler on normal distribution
• measurements = z-scores
• = how many standard deviations above or below a data point is
• z = (x - mean) / standard deviation
• no units, mean of all z-scores = 0, standard deviation of all = 1

Question 25

K-th percentile (Pk)

Answer 25

k% data is less than it k percent of observations are less than the value ex. P99 = 99th percent: # which 99% of data is below Q1 = P25 ~x = P50 Q3 = P75 93rd percentile = 7% of students scored higher than you