Lesson 1.7 - How Did I Do?
How well did you do on the Chapter 1 Test? How well did you do relative to your classmates?
1. If Mr. Oruduñez took the Chapter 1 Test and got a 75, give a reason where this would be
a good score. Then, give an example of a reason this could be a bad score.
Good
Bad
si isabove so whichisaboveaverage
si isbadbecause it isn'taBorA
Here are the results of a random sample of 20 of the chapter 1 tests, along with a dot plot
and summary statistics.
Scores
61
65
65
73
75
77
78
78
79
80
80
80
80
81
81
88
To
2. Neil Scored a 65. What is Neil’s percentile?
15thpercentile
E
89
93
98
99
300 20
15 9
3. Was Neil above or below the mean? By how many points? By how many standard
deviations (for calculation sake, assume SD = 10).
Belowthemean
by 15points
Belau by1.5
standard deviation
4. Claire scored an 88. What is Claire’s percentile?
EE
80th percentile
180020x
80 x
5. Was Claire above or below the mean? By how many points? By how many standard
deviations?
baby 8 standard dewan
themean
above
bygpt
above
A z-score is defined as the number of standard deviations above or below the mean.
6. Write a formula for calculating a z-score.
!=
soigne
7. Porky scored a 98 on the Chapter 1 Test. Find (with your formula) and interpret the zscore.
2
985
1.8
DOTPLOT A
DOTPLOT B
DOTPLOT C
2
Original
scare
1. What happened to every data point to move from dotplot A to dotplot B?
Allthe data pantsmoved so ptsdown Its a shift
2. What happened to shape, center, and variability when this happened?
Shape:
PlotAMean 80
Bmean O
Center: Plot
Same
spread
K
Variability
so
Variability: thesame
SD
isthesame
different
median
3. What happened to every data point to move from dotplot B to dotplot C?
eachdatapointwasascared
4. What happened to shape, center, and variability when this happened?
Shape:
Center: same mean
same
Variability: change
Itwas divided by
bothzero
SP
5. What is the mean and standard deviation of the distribution of z-scores? Will this be true
for any distribution?
Mean is 0
SPis 1
Yes beofthe
formula
Example: Daffy took an Algebra test and got a 96%. The class average was a 94% with a SD of
3%. Bugs took an AP Calc test and got a 83%. The class average was 70% with a SD of 5%.
Daffy says that he did better but Bugs disagrees on who did better relative to their exam.
Explain.
2 Score
Ymca
Neil 90,31
Cain
f
EY Es
Lesson 1.7 - Describing Location in a Distribution BATS
1.
2.
3.
Find and interpret the standardized score (z-score) of an individual value in a distribution of data.
Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and variability of
a distribution.
Standardize values to make comparisons across different data sets.
BAT #1 & #3 - Standardized Values (z-scores)
BAT #2 - Constant Effects
Given a distribution if you,
YY.no
!=
“Valuein context
deviations abovebelow
-Add/Subtract each value by a constant “a”
is
standard
the mean.”
● Shape/Variability → same
● Center → shift ordam
by a
up
All standardized distributions have a mean of
and SD of
.
o
Multiply/Divide each value by a constant “b”
1
*Use to compare things from
sets.
different
data
● Shape →same
● Center/Variability →
N
byb
Application Problems
1. According to an article on Yahoo! news, you should change your sheets every 7 days…at minimum. To
investigate the sheet changing habits of adults, a random sample of 20 adults reported how often they change
their sheets using an anonymous survey. Here is a dotplot and summary statistics of the results.
day
week
a. Suppose you convert the time before changing sheets from days to weeks. Describe the new shape,
mean, and standard deviation of the distribution of time before changing sheets in weeks.
shapestays same
will change h
Variability
SAY 35 5weeks
I
mean
2 Glued
b. The adults in the study are given an article explaining the health benefits that would arise from changing their
sheets more often. After reading the article each person agrees to change their sheets one week sooner than
they used to. How does the shape, center, and variability of this distribution compare with the distribution of
time in part (a)?
Sweets shapeunchanged
meant
8D
Leek
variability
same
c.
Now suppose you convert the time before changing sheets from part (b) to z-scores. What would be the
shape, mean, and standard deviation of this distribution? Explain your answers.
Mean
O
sp t
shape
same