-brief description should include its shape and numbers describing its center and spread,
based on inspection of the histogram or stemplot
-graphs are aide to understanding no the answer
-measures of center are the mean(average value) and median(middle value)
-to figure out mean: mean . Add their values and divide by the number of observations. If
the n observations are , ,…..,, their mean is
= or in more compact notation: =
is sigma. Is the mean short for add them all up.
: the bar on top indicates the mean of all the x values.
: keep the n observations separate. Not necessarily indicate order or any other special
facts about the data
-the mean is sensitive to the influence of a few extreme observations ex. outliers. Since
mean can’t resist the influence of extreme values, it’s not a resistant measure of center.
-median: formal version of midpoint of a distribution. Half the observations are smaller
than the median and the other half are larger than the median. Rule for finding the
1. arrange all values in order of size, from smallest to largest.
2. if the number of observations n is odd, the median M is the center value in the ordered
list. Find the location of the median by counting (n + 1)/2 observations up from the bottom
of the list
3. if the number of observations n is even, the median M is the mean of the two center
observations in the ordered list. The location of the median is again (n+1)/2 from the bottom
of the list.
- if the distribution is exactly symmetric, the mean and median are exactly the same
-don’t confuse the “average” value of a variable (the mean) with its “typical” value, which we
might describe by the median
-quartiles: elaborate more on the spread or variability of the incomes and drug potencies as
well as their centers.
-most useful descriptions explain both a measure of center and measure of spread
-describe spread or variability, by giving several percentiles
-median divides the data in two, we call the median the 50th percentile. Upper quartile is
the median of the upper half of the data. (same for the lower quartile, lower half)
-quartiles divide the data into 4 equal parts
-pth percentile of a distribution is the value that has p percent of the observations fall at or
-to calculate percentile, arrange values in increasing order and count up the required
percent from the bottom of the list. There is not always a value with exactly p percent of the
data at or below it.
-quartiles Q1 and Q3: to calculate the quartiles:
1. arrange values in increasing order and locate median M in the ordered list.
2. first quartile Q1 is the median of the values whose position in the ordered list is to the
left of the location of the overall median.
3. third quartile relates the median on the right.