Download Hand-span Measurements 1. Get a ruler and measure your hand-span

Secondary Math I
Name ________________________
Hand-span Measurements
STANDARD DEVIATION is the average of the distances that the data deviate from the mean. 1. Get a ruler and measure your hand-span (the distance from the tip of
your thumb to the tip of your little finger when you spread your fingers).
Measure to the nearest half-centimeter.
2. For your group of four people, record the hand spans of all members of
the group for a total of four measurements.
_________________ _________________ _________________ _________________
3. Create a centimeter number-line for the group to cover the hand-span widths of the members of your
group. Make a dot plot of the hand-spans of the four members of your group. Write initials above the dots
to identify the member of your group. NOTE: Everyone in the group must do this for everyone in the
group.
HAND-SPANS
4. Find the mean hand-span for your group. Mark the mean hand span on your dot plot with a wedge Δ below the number line. Mean _________
5. For each hand-span measurement, determine how far from the mean each measurement is. (These are
called DEVIATIONS.) All hand-spans smaller than the mean will have negative values and all hand
spans larger than the mean will have positive values.) Record your work in this table:
6. Now create a second number-line below. Put a dot on the new number for each person’s distance from
the mean or DEVIATION (recorded in the table above) on the number line below. Again, write initials
above the dots on the number line.
7. Find the mean of these deviations (distance from the mean.) Place the wedge on the number line to
indicate the mean.
8. What is the sum of the deviations from the mean for your group? _______________
Note that the sum of the deviations (from the mean) always equals ___________. Why?
9. Using the definition in the text box above fill in the blanks: The standard deviation is the ___________
of how far the data points are from the mean or how far they DEVIATE from the mean. But to find the
mean you must sum the deviations, but the deviations always sum to __________. Therefore, the mean
would always be ___________ no matter how the data deviates.
10. To solve this problem mathematicians square every deviation. This allows all the data to be positive
so that the sum will not be equal to 0. Square the deviations for the hand span measurements and record
in this table.
11. Find the mean of those squared deviations: ____________ square cm. This is called the variance.
Why is it square cm instead of cm?
12. The variance is not the standard deviation because it was calculated using the squares of the
deviations instead of the deviations. The final step to get the standard deviation is to take the square root
of the variance. Why do we need to take the square root?
Find the standard deviation by taking the square roots of the variance: __________ cm. (Why is it not
square cm?)
13. Here are the scores for 3 students on the quizzes for the quarter. Complete the table for each.
A: 10, 10, 10, 10, 10
B: 8, 9, 10, 11, 12
C: 7, 9, 10, 11, 13
Mean
Median
Range
IQR
Standard
Deviation
A
B
C
14. Who is the better student? Be sure to use the words mean, median, range, IQR, and standard
deviation in your answer.
15. What do you think the standard deviation tells you?
16. Compare these test scores for Joe and Sam by finding the mean of each. What do you notice about
Joe’s scores compared to Sammy’s using the means?
Joe: 60, 68, 69, 78, 90, 95, 100
Sam: 78, 78, 79, 79, 82, 82, 82
Who is the better student? Explain using standard deviation why you think so.