Download Math 2000 Test 1 Cheat Sheet

Math 2280 Test 1 Cheat Sheet
When figuring the class width to use when constructing a frequency distribution
highest - lowest
figure
. Then round up. The first class begins with the lowest data
number of classes
value.
For an odd number of data the median is the middle value.
For an even number of data the median is the average of the middle two values.
Mean  x 
x
n
Definition formula for variance of samples: s 2 
 (x  x )
2
n 1
n x  ( x ) 2
2
Computation formula for variance: s 2 
n(n  1)
Chebyshev’s Theorem:
3
At least , or 75% of values lie in the interval x  2s to x  2s .
4
8
At least , or 88.9% of values lie in the interval x  3s to x  3s .
9
15
At least
, or 93.75% of values lie in the interval x  4s to x  4s .
16
Empirical Rule:
Approximately 68% of values lie in the interval x  s to x  s .
Approximately 95% of values lie in the interval x  2s to x  2s .
Approximately 99.7% of values lie in the interval x  3s to x  3s .
z
xx
s
x  x  sz
For box plots you use the five number summary: least, Q1 , Q2 , Q3 , biggest
Q2 is the median
Q1 is the median of the values to the left of the median
Q3 is the median of the values to the right of the median
To find the pth percentile you calculate p% of the number of values.
(a) If the result is not a whole number you round up to the next whole number
and this gives the position of the pth percentile.
(b) If the result is a whole number, say 10, then the pth percentile is the mean of
the 10 and 11th values.
th
Weighted mean =
 wx
w