Transcript Annual Incomes of 10 Families

Why do we need the standard deviation?
1- The standard deviation reflects dispersion of data values,
so that the dispersion of different distributions may be
compared by using standard deviations.
2- The standard deviation permits the precise interpretation of
data values within a distributions.
3- The standard deviation, like the mean, is a member od a
mathematical system which permits its use in more advanced
statistical considerations.
EMPIRICAL RULES
1- About 68% of the values will lie within 1 standard deviation of the mean, that
is, between x̄ - s and x̄ + s;
2- About 95% of the values will lie within 2 standard deviation of the mean, that
is, between x̄ - 2s and x̄ + 2s;
3- About 99.7% of the values will lie within 3 standard deviation of the mean,
that is, between x̄ - 3s and x̄ + 3s;
BOX PLOT
A Box Plot is a graphical summary of data that is based on five number summary.
To construct a box plot use the following STEPS
1- A box is drawn with the ends of the box located at the first (Q1)
and third quartile ( Q3)
2- A vertical line is drawn in the box at the location of the median.
3- By using IQR=Q3-Q1, limits (also called fences) are located.
The limits for the box plot are Q1 - 1.5*IQR and Q3 + 1.5*IQR
DATA OUTSIDE THESE LIMITS ARE CONSIDERED OUTLIERS
4- The dashed lines (also called whiskers) are drawn from the ends of the box to the
smallest (L) and highest (H) values inside the limits computed in STEP 3
5- Finally, the location of each outlier is shown with a symbol
*