Transcript Summer Assignment ANSWERS

Summer Assignment
2. What is Statistics?
 Statistics is the science of data. It is used to gain insight and to draw
conclusions.
3. What is the difference between categorical and quantitative
variables? Give examples of each.
 Categorical variables places individuals into groups such as gender,
religion and color. Finding the average of these things have no
meaning.
 Quantitative variables have numerical values such as price, GPA and
height. Finding the average has meaning.


Age is quantitative. Ex. Average age of a sophomore is 14.5 years.
Year is categorical. Ex. Average year is 1982.4???? That makes no sense!!!
4. Quantitative variables are broken down into discrete and
continuous variables. Give three examples of each.
 Discrete variables are countable values, such as the number of
children in a family, the number of students in a classroom or the
number of calls in one day.
 Continuous variables have an infinite amount of values for example
temperature, height and weight.
5. What is the difference between a bar graph and histogram?
 Bar graphs are used to represent categorical data. They bars never
touch.
 Histograms are used to represent quantitative data. The bars must
be touching and the equally sized classes must be created.
 The similarity is that they are both frequency graphs.
6. What is a circle graph used for and can it always be used in place
of a bar graph?
 Circle graphs are used to display the percent values of categorical
variables ONLY is the sum of all the percents is 100% at a set point
in time.
 A circle graph can always be used in place of a bar graph as long as
all percents add up to 100%. If this does no occur, create an other
category.
7. When is a time plot appropriate and what is meant by a trend
and a seasonal variation of a time plot?
 Time Plots are used when variables are measured in intervals over
time. Always mark the time scale on the x-axis.
 Trends are upward and downward patterns.
 Seasonal Variation are patterns that repeat themselves.
8. What does it mean for the shape of a distribution to be
a.
Normal means the distribution is symmetric on both sides. It is also
called bell-shaped.
b. skewed right means the curve has a long tail to the right.
c. skewed left means the curve has a long tail to the left.
9.You received a standardized test score report stating that you
were in the 80th percentile of all test takers. Explain what this
means.
 This means that 80% of everyone who took the test scored less than
or equal to your score. The other 20% scored higher than you did.
10. In considering a frequency distribution, is it a good idea to have
overlapping classes such as 10-20, 20-30, 30-40? Explain.
 No, some data points will be counted twice and this makes the
graph meaningless.
11. Can histograms be drawn using vertical and horizontal bars or
only one way? Explain.
 Histograms can only be drawn vertically. The
explanatory/independent variable must be on the x-axis.
12. What is an Ojive and what is it used for?
 An ojive is a relative cumulative frequency graph which gives
information on the relative standing of an individual. The ojive
gives us the percentile of individuals with respect to all the others.
13. Define
a.
Mean is the average of a set of numbers. Add all the
numbers and divide by how many numbers we have.
b.
Median is the middle number when all the numbers are put
in order. If there are two middle numbers, find the average
of the two.
c.
Mode is the number that appears the most frequently.
d.
Range is the largest number minus the smallest number.
14.
b. Describe the center, spread, shape, outliers, gaps and clusters
from the graph.
Center: between $1 and $2
Spread: $0 - $10
Shape: Right Skewed
Gaps: From $7 - $9
Clusters: From $0 to $6 and $10
Outliers: $10
# 19
Ojive Extra Practice
Relative Cumulative Frequency Distribution
Finding Relative Frequency
Class
Frequency
40-44
2
45-49
6
50-54
13
55-59
12
60-64
7
65-69
3
Total
43
AP Statistics, Section 1.1, Part 4
28
Finding Relative Frequency
Class
Frequency
Relative
Frequency
40-44
2
2/43=4.7%
45-49
6
6/43=14.0%
50-54
13
13/43=30.2%
55-59
12
12/43=27.9%
60-64
7
7/43=16.3%
65-69
3
3/43=7.0%
Total
43
AP Statistics, Section 1.1, Part 4
29
Finding Cumulative Frequency
Class
Frequency
Relative
Frequency
Cumulative
Frequency
40-44
2
2/43=4.7%
2
45-49
6
6/43=14.0%
8
50-54
13
13/43=30.2%
21
55-59
12
12/43=27.9%
33
60-64
7
7/43=16.3%
40
65-69
3
3/43=7.0%
43
Total
43
AP Statistics, Section 1.1, Part 4
30
Finding
Relative Cumulative Frequency
Class
Frequency
Relative
Frequency
Cumulative
Frequency
Relative
Cumulative
Frequency
40-44
2
2/43=4.7%
2
2/43=4.7%
45-49
6
6/43=14.0%
8
8/43=18.6%
50-54
13
13/43=30.2%
21
21/43=48.8%
55-59
12
12/43=27.9%
33
33/43=76.7%
60-64
7
7/43=16.3%
40
40/43=93.0%
65-69
3
3/43=7.0%
43
43/43=100%
Total
43
AP Statistics, Section 1.1, Part 4
31
Percentiles
Class
Relative
Cumulative
Frequency
40-44
2/43=4.7%
45-49
8/43=18.6%
50-54
21/43=48.8%
55-59
33/43=76.7%
60-64
40/43=93.0%
65-69
43/43=100%
 It is easy to see the
percentiles at the breaks.
 “A 64 year old would be at
the 93rd percentile.”
 What do you do for a 57 year
old?
Total
AP Statistics, Section 1.1, Part 4
32
Ogives (o-JIVE) or
“Relative Cumulative Frequency Graph”
Class
Relative
Cumulative
Frequency
40-44
2/43=4.7%
45-49
8/43=18.6%
50-54
21/43=48.8%
55-59
33/43=76.7%
60-64
40/43=93.0%
65-69
43/43=100%
Total
33
AP Statistics, Section 1.1, Part 4
 Bill Clinton was 46 years old when inaugurated.
 He falls in the 10th percentile.
 Means: 10% of all US presidents were the same age or younger
than Bill Clinton when inaugurated.
 What age corresponds to the 60th percentile?
 57 years
 Means: 60% of all presidents were 57 years or younger when
inaugurated.
What is the center of the distribution?
50%-56 years
Review
Data
Categorical
 Places individuals into groups
Quantitative
 Created numerical values
 Ex. Male or female
 Ex. Price
Color
 Religion
 **Year


Height
 GPA
 **Age
Discrete
•Can be counted
•# of children in
a family
•# of students in
a class
Continuous
•Can assume all
values b/w any 2
specific values.
Obtained my
measuring.
•Temperature
•Height
•Weight
Graphs
 Categorical:


Bar Graph
Circle Graph
 Quantitative

Dot Plot-Small # of data
Spread
Outliers  Stem Plot-Small # of data
Center  Histogram-Larger # of data
Shape
Ojive tells us what percentile an individual falls into.
Time Plot plots variables against time.
Time is always on the horizontal axis.
2 Quantitative variables-scatterplot
2 categorical variables-side by side bar graph