LOWELL CATHOLIC HIGH SCHOOL
Summer Math
ENTERING
HONORS STATISTICS
Exploring Data
Population vs. Sample
A population is any entire collection of people or objects from which we may
collect data. It is the entire group of interest that is used to describe or draw
conclusions about.
Example:
Examining all registered voters in Lowell, MA
A sample is a group of people or objects selected (usually randomly) from a
larger group (the population). By studying the sample it is hoped to draw valid
conclusions about the population.
Example:
Examining registered voters on certain streets in Lowell, MA
Example:
Writingbelow
a ratiodescribe
in simplest
formor a population? Circle one.
Does
each situation
a sample
10 5

5 : 12
5 to 12
24 12
1) Students survey a random selection of professors at a college to determine how
many courses they teach per semester.
Population
Sample
2) Teachers reviewed the final exam grades of all graduating seniors.
Population
Sample
3) The government performs a study to review the votes collected in Massachusetts
for the U.S. Presidential Election.
Population
Sample
4) A small business reviews the sales of each year it has been operating.
Population
Sample
Measures of Center
Mean, Median and Mode
The mean is the average value of a data set.
To find the mean of a data set, find the sum of the data values then divide by the
number of data values.
MEAN = . sum of data values .
number of data values
The median of a set of data is the middle value (odd number of values) or the
average of the two middle values (even number of values) when the set is ordered
from least to greatest
The mode of a set of data is the value or values that occur most often. To determine
the mode of a set of data, count the number of times each data value appears. If no
values repeat, there is no mode or conclude that every value is the mode.
Determine the mean, median and mode of each set of data below:
5) Below are the pizza prices (per slice) of various local pizza restaurants:
$2.20, $2.30, $2.20, $2.75, $2.60, $2.50, $2.25, $2.20, $2.95, $2.60, $2.20
6) Below are the number of emails various professors receive daily at a local
university:
37
25
24
37
42
28
27
28
25
29
41
25
7) How many points do football teams score in the Super Bowl? Below are the
total number of points scored by both teams in each of the first 20 Super Bowl
games:
45
46
47
37
23
66
30
50
29
37
27
47
21
44
31
47
22
54
38
56
Histograms
A histogram uses adjacent bars to show the distribution of a quantitative
variable. Each bar represents the frequency (or relative frequency) of values
falling in each bin.
The x-axis represents the students’ scores and the y-axis represents the
frequency if each grade. The grades are categorized on the x-axis using
classes (or bins)
Use the figure above to answer the following questions?
8) Approximately how many students scored between a 40 and a 60?
9) What grade range was most frequent on the final exam?
10) Approximately how many students scored between an 80 and a 100?
11) Approximately how many students took the final exam?
Stem-and-Leaf Plots
A stem-and-leaf plot shows quantitative data values in a way that sketches
the distribution of the data. If you turn a stem-and-leaf plot on its side, it looks
very similar to the shape of a histogram.
Data values:
19, 22, 25, 26, 27, 28, 29, 30, 34, 36, 37, 42,
43, 44, 46, 48, 48, 49, 52, 53, 55, 57, 58, 62
Given the stem-and-leaf plot below, answer the following questions:
12) What are the date values?
List in numerical order.
16) What is the minimum value?
13) What is the mean?
17) What is the maximum value?
14) What is the median?
18) What is the range (Range = Max
value – Min value)?
15) What is the mode?
Percents and Decimals
Example 1: Change a decimal to a percent
What is 0.35 as a percent?
0.35 X 100 = 35%
Example 2: Change a percent to a decimal
What is 46% as a decimal?
46  100 
46
 0.46
100
Example 3: Change a fraction to a percent
What is
27
as a percent?
100
27
 100  27%
100
19) Change 63% to a decimal
and a fraction.
20) Change 0.50 to a fraction
and a percent.
51
to a percentage
100
and decimal.
21) Change
2
to a decimal and
5
a percentage.
22) Change
Bar Graphs
A bar graph uses rectangular bars to organize and display data. It is made
up of these individual parts:
 A title
 A horizontal axis with labels
 A vertical axis with labels
 An interval
 Data
Suppose you were asked to construct a bar graph that organizes and displays
the data shown in the table.
23) What title would you choose for the bar graph?
24) What label would you choose for the horizontal axis?
25) What label would you choose for the vertical axis?
26) What interval would you use? Explain.
27) Use your answers from problems 23 – 26 to construct a bar graph for the
data in the table
Graphs
A circle graph uses parts of a circle to organize and display data.
The part of this graph labeled 65% makes up
234  of the graph because
65% of 360 = 0.65 X 360 = 234
The part of this graph labeled 35% makes up
126  of the graph because
35% of 360 = 0.35 X 360 = 126
You can check your work by finding the sum of the parts:
234  + 126  = 360 
Examine the circle graph and answer the following questions:
28) Name the fraction in simplest form, the decimal and the number of degrees
that represent Action Movies.
29) Name the fraction in simplest form, the decimal and the number of degrees
that represent Comedy Movies.
30) Name the fraction in simplest form, the decimal and the number of degrees
that represent Drama Movies.
31) Describe how a circle graph can be checked for accuracy
Graphs
Suppose two six-sided dice numbered 1 through 6 are tossed at the same
time and the outcomes of the dice are added to create a sum.
For example, if the outcome on the first die is 3 and the outcome on the
second die is 4, then the sum of the outcomes on the dice is 3 + 4 = 7.
The frequency table shows the number of different ways various sums can be
made by tossing two six-sided dice.
Answer the following questions about the frequency table shown above:
32) What is the greatest possible
sum that can be created by
tossing two six-sided dice?
35) Based on the table, which sum
will occur most often when two
six sided dice are tossed? Which
sums will occur least often?
33) What is the least possible sum
that can be created by tossing
two six-sided dice?
34) How many tosses of the dice
are shown in the frequency
table?
36) What interval was used to
create this frequency table? Is
there a better interval that could
have been used? Explain.
Mean
The mean is the average value of a data set.
To find the mean of a set of data, find the sum of the data values, then divide
by the number of data values.
MEAN = . sum of data values .
number of data values
Examine the data shown in the table. The data show the average amount of
precipitation received each month in Miami, Florida:
Answer the following questions about the data shown in the table above:
37) What useful information do the labels in the table provide?
38) How many data values does the set contain?
39) What is the sum of the data values?
40) Identify the steps to follow to determine the mean of the data set.
41) What is the mean amount of precipitation received each month in
Miami, FL? Round your answer to the nearest hundredth inch.
Median
The median of a set of data is the middle value when the set is ordered from
least to greatest or the average of the two middle values.
Examine the data shown in the table. The data show the inauguration ages of
selected U.S. presidents:
Answer the following questions about the data in the table shown above:
42) Order the data values from least to greatest.
43) Does the set of data have an even number or an odd number of data
values?
44) How is finding the median of a data set with an even number of values
different from finding the median of a data set with an odd number of
values?
45) What is the median inauguration age of the presidents shown in the table?
Mode
The mode of a set of data is the value or values that occur most often.
To determine the mode of a set of data, count the number of times each value
appears.
Examine the data shown in the table. The data show elevation in feet above
sea level of selected U.S. cities:
Answer the following questions about the data in the table shown above:
46) How many different data values appear in the table? What are those
values?
47) How could you determine the mode of the data?
48) What is the mode of the data?
49) Suppose each value in a set of data occurs the same number of times.
What is the mode of the set of data?
Range
The range of a set of data is the difference between the maximum value and
the minimum value.
RANGE = Max Value – Min Value
Examine the data shown in the table. The data show the lengths in miles of
selected rivers in North America:
Answer the following questions about the data table shown above:
50) What is the longest river shown in the table? What is its length?
51) What is the shortest river shown in the table? What is its length?
52) How could you determine the range of the data?
53) What is the range of the data?
54) In order to find the range of a set of data, is it necessary to order the data
from least to greatest?
Data and Statistics
Examine the data shown in the table below. The data show the locations and
heights in feet of famous waterfalls:
Answer the following questions about the table shown above:
55) What data are represented in the table?
56) How many data values does the table display?
57) When should you break the vertical axis of a bar graph? Explain.
58) What is the mean of the data? Round to the nearest whole number.
59) What is the median of the data?
60) What is the mode of the data?
61) What is the range of the data?