Transcript Introduction to Standard Deviation

Introduction to
Standard Deviation
Honors Analysis
Create a stem plot for each set of test
scores:

78, 94, 82, 91, 85, 88, 92, 81, 77, 92

54, 102, 87, 92, 68, 104, 101, 62, 96, 94
Stem Plots

The FIVE POINT SUMMARY for a set of
data includes:
1)
2)
3)
4)
5)
Minimum value (100% of data above)
First quartile (Q1) – Median of first half
Median (Q2) – (50% of data above)
Third quartile (Q3) – Median of second half
Maximum value
Five Point Summary

The INTERQUARTILE RANGE (IQR) can
be found by subtracting Q1 from Q3:
IQR = Q3 – Q1 (50% of data between
these values)
Interquartile Range

A BOX PLOT depicts the five point
summary of a data set:
Box Plot (Box & Whisker)

Enter data into calculator:
◦ STAT  EDIT (enter list into L1, L2, etc.)

To calculate 1-Variable Statistics:
◦ STAT  CALC  1-Var Stats
◦ (includes sum, mean, median, etc.)
The Graphing Calculator

Enter data into lists (STAT  EDIT)

Turn Stat Plots ON
◦ 2nd  STAT PLOT  PLOT 1 (or 2)
◦ Turn ON
◦ Select list for data (Xlist)

To Graph: ZOOM  ZOOMSTAT
Box Plots on Calculator
Create a BOX PLOT comparing the test
data:

78, 94, 82, 91, 85, 88, 92, 81, 77, 92

54, 102, 87, 92, 68, 104, 101, 62, 96, 94
Compare the box plots… what do you
notice?
Box Plot
1
𝑛
𝑛
|𝑥𝑖 − 𝑥 |
𝑖=1
Mean Deviation
1) Find the difference of each value and the
mean (don’t lose the sign!!)
2) Find the sums of the differences from
the mean
3) Divide by the number of total values
Mean Deviation

78, 94, 82, 91, 85, 88, 92, 81, 77, 92

54, 102, 87, 92, 68, 104, 101, 62, 96, 94
How are the mean deviations different?
What does this tell you?
Calculate the Mean Deviation
𝜎=
1
𝑛
𝑛
(𝑋𝑖 −
𝑖=1
Standard Deviation
2
𝑋)
1) Find the difference between each value
and the mean
2) Square the differences
3) Sum the squares
4) Divide by the number of values
This result is called the VARIANCE
5) Take the square root – this is the
standard deviation
Standard Deviation