Transcript Day 5

Ch. 4: Average &
Standard Deviation
• Computing the average:
– Sum of the values divided by the number of
values.
– Example: What is the average of the ages of
the students in the first row?
• One measure of center is the average
• Another measure of center is the median
– The median is the 50th percentile of the data.
In other words, 50% of the data is greater
than the median and 50% is less than the
median. More simply stated, the median is
the middle value when the data is put in order
from least to greatest.
– Example: What is the median age in the first
two rows of students?
• First order the data.
• If it is an even number of values, take the average
of the 2 middle numbers. If it is an odd number of
values, pick the middle value in the ordered data.
Cross-sectional versus
Longitudinal Studies
• Cross-sectional studies allows one to
compare subjects to each other at one
point in time.
• Longitudinal studies allows one to follow a
subject over time and compare them to
themselves over time.
• Examples: NHANES vs. Framingham
Heart Studies
Comparing Averages and Medians
• The average is to the right of the median
whenever the histogram has a long right
tail.
• Example: US Census 2004
• Median income: $45,996
• Average income: $62,083
Standard Deviation
• How far data is from their average.
Describes the spread of the data around
the average.
• Roughly 68% of data are within 1 SD of
the average.
• Roughly 95% of data are within 2 SDs of
the average.
• These 2 statements are true most of the
time but not always.
Calculating the SD
1. Find the average.
2. Find the deviation from the average for
each data point.
3. Square the deviations.
4. Take the mean square of the square
deviations (MS).
5. Take the square root of the MS (RMS).
• Example: 4, 4, 4, 4, 7