Statistics - Descriptive Statistics Part II
what are 4 common measures of spread?
1. Range 2. Interquartile Range (IQR) 3. Standard Deviation 4. Variance
given: 15, 4, 3, 8, 15, 22, 7, 9, 2, 3, 3, 12, 6 what is : interquartile range range variance standard deviation minimum maximum
10.5 20 33.9 5.8 2 22
Provided the values below, what is the range? (The range should just be a single number) 5, 10, 3, 8, 12, 4, 1, 2, 8
11
What is the range associated with the following dataset? 1, 5, 10, 3, 8, 12, 4, 1, 2, 8
11
given: 15, 4, 3, 8, 15, 22, 7, 9, 2, 3, 3, 12, 6 what is n median first quartile third quartile mean mode
13 7 3 13.5 8.4 3
1, 5, 10, 3, 8, 12, 4 variance?
13.55
Provided the values below, what is the value of the first quartile? Remember the first quartile is the median number (middle number) of the first half of the numbers when put in ranked order. Ranked order for this dataset is 1,1,2,3,4... 1, 5, 10, 3, 8, 12, 4, 1, 2, 8
2
Provided the values below, what is the the value for the first quartile? 5, 10, 3, 8, 12, 4, 1, 2, 8
2.5
1, 5, 10, 3, 8, 12, 4 variance = 13.55 std deviation?
3.68
Provided the values below, what is the value of the median? (this is the same as the second quartile) 1, 5, 10, 3, 8, 12, 4, 1, 2, 8
4.5
Provided the values below, what is the value of the median? (this is the same as the second quartile) 5, 10, 3, 8, 12, 4, 1, 2, 8
5
what is the most common ways to measure spread of data
5 number summary
Provided the values below, what is the value of the third quartile? 1, 5, 10, 3, 8, 12, 4, 1, 2, 8
8
Provided the values below, what is the the value for the third quartile? 5, 10, 3, 8, 12, 4, 1, 2, 8
9
what are the 5 numbers in 5 number summary?
Minimum: The smallest number in the dataset. Q1: The value such that 25% of the data fall below. Q2: The value such that 50% of the data fall below. Q3: The value such that 75% of the data fall below. Maximum: The largest value in the dataset.
how to calculate interquartile range?
Q3-Q1
which quartile is also the median?
Second Quartile
what is Q1 in 5 number spread?
The value such that 25% of the data fall below.
what is Q2 in 5 number spread?
The value such that 50% of the data fall below.
what is Q3 in 5 number spread?
The value such that 75% of the data fall below.
what is a good graph to represent spread?
a histogram
If a dataset has a standard deviation of zero, what are datapoints like?
all must be same
first step in creating a histogram?
binning
what type of plot is good for comparing the spread of 2 sets of data?
box plot
If we measure the variance associated with our sales in dollars for each month for 3 years, what are the units associated with the variance?
dollars^2
in finance what does higher stand dev imply?
higer risk
what is spread?
how far our data is spread from each other
how to calculate the Range?
max - min
left-skewed: what is mean vs median relationship <=>
mean < median
normal distribution: what is mean vs median relationship <=>
mean == median
right-skewed: what is mean vs median relationship <=>
mean > median
Q1 is median of which data points?
median from Minimum to Q2(median)
Q3 is median of which data points?
median from Q2(median) to Maximum
do you use Q2 to calculate Q1 or Q3 ?
no
when comparing 2 datasets, given std dev. can you infer mean of each one?
no
when comparing 2 datasets, given std dev. can you infer range?
no
how to calculate the 5 number summary?
order values get min and max get middle value (median) Q2 get Q1 (median on left side of Q2) get Q3 (median on right side of Q2)
how do you calculate interquartile range?
q3-q1
how do you measure the spread of datapoints using a single value?
std deviation or variance
How to calculate variance
sum of the data point(s) minus the mean squared divided by the number of values 1/n *∑_n(x_i − x¯)^2
What is standard deviation?
the average distance of each observation from the mean
how do you calculate the standard deviation?
the square root of the variance ie) sqrt (mean of (x-x_mean)^2))
what about units considerations for variance/std dev?
units must be same for comparisons variance is units ^2 stdev is in units units
if 2 datasets have same variance do they also have same standard deviation?
yes
