STATISTICS REVIEW
COPY DOWN THIS DATA:
HEIGHTS OF MS. G’S
HOMEROOM STUDENTS:
65
65
65
69
67
63
73
60
60
63
71
74
63
64
66
65
Psst… you
should have
started the
Do Now!
COLUMN GRAPHS,
FREQUENCY TABLES,
FREQUENCY HISTOGRAMS
10 min
lesson,
5 min exit
slip
COLUMN GRAPHS MEASURE DISCRETE DATA!
STEP 1: FREQUENCY TABLE (variable x, freq. y)
Height
Frequency
60
2
63
3
64
1
65
4
66
1
67
1
69
1
71
1
73
1
74
1
COLUMN GRAPHS MEASURE DISCRETE DATA!
STEP 2: COLUMN GRAPH
Frequency of Heights (in.) of Ms. Griffith’s Homeroom
5
4
3
2
1
0
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
PROS AND CONS OF COLUMN GRAPHS
Pros
Cons
 Super easy to make
 Can take a long time
 Easy to read
 Hard to see trends for
groups of data… (for
example, is it
coincidence or
important that only 1
person is 64”?)
 Even for middle schoolers!
 Abundantly clear
FREQUENCY HISTOGRAMS MEASURE
CONTINUOUS OR GROUPED DATA!
STEP 1: Make a Frequency Table with Intervals
Height Interval (inches)
Frequency
60 - 62
2
63 - 65
8
66 - 68
2
69 - 71
2
72 - 74
2
5 is the ideal number of intervals!
The intervals have to be equal in size!
(Here, I have five intervals with 3 in. each!)
FREQUENCY HISTOGRAMS MEASURE
CONTINUOUS OR GROUPED DATA!
STEP 2: Make a Frequency Histogram with Intervals
Frequency within Homeroom Height Intervals
9
8
7
6
5
4
3
2
1
0
60 - 62
63 - 65
66 - 68
69 - 71
72 - 74
The bars have to be equal width and touch each other!
RECAP AND COMPARE/CONTRAST
Column Graphs
 Start with freq. table
 List every answer
 Write down frequency
 Draw the column graph
 Bars do NOT touch
 Bars have equal width
Frequency Histograms
 Start with freq. table
 5 intervals of equal width
 Frequency is per group
 Draw the histogram
 Bars touch (covers all
possible data)
 Bars have equal width
EXIT SLIP: COLUMN GRAPHS & HISTOGRAMS
Misty asked Mr. Caine’s homeroom how many hours they
typically slept on a Friday night. Here were their responses:
4
8
4
9
5
9
6
9
6
10
6
10
a) Make a frequency table for this data.
7
10
7
12
8
Answers are on the next
slide!! (No room here)
b) Sketch a column graph for this data.
c) Make a frequency table with intervals of 2 hours each (e.g.,
4-5 hours) for this data.
d) Sketch a frequency histogram for this data.
EXIT SLIP ANSWERS:
COLUMN GRAPHS & HISTOGRAMS
Make a Frequency Table
Sleep (Hours)
Frequency
4
2
5
1
6
3
7
2
8
2
9
3
10
3
12
1
Sketch a Column Graph
Frequency
3
2
1
0
4
5
6
7
8
(c) And (d) are on the next slide… ran out of room!
9 10 11 12
EXIT SLIP ANSWERS:
COLUMN GRAPHS & HISTOGRAMS
Make a Frequency Table
with Intervals (group)
Sketch a Frequency
Histogram
Sleep Time (hours) Frequency
Frequency
4–5
3
6
6–7
5
5
8–9
5
10 – 11
3
12 - 13
1
4
3
2
1
0
4-5
6-7
8 - 9 10 - 11 12 - 13
MEAN,
MEDIAN,
MODE,
STANDARD DEVIATION
8 min
lesson,
3 min exit
slip
MEAN MEASURES THE EXPECTED VALUE.
Add them up!
Called “x-bar” –
shows up as the
mean on your
calculator in
“One-Var Stats”
All the answers
times the
frequency of
each answer.
Number of terms/answers
TRY OUT MEAN WITH THE FORMULA! _______
Height in inches (xi)
Frequency
Product (fixi)
60
2
120
63
3
189
64
1
64
65
4
260
66
1
66
67
1
67
69
1
69
71
1
71
73
1
73
74
1
74
SUM
16
1053
1053/16 = 65.8” (5’ 5.8”)
BUT WHAT ABOUT MEAN FOR GROUPS??
___
That’s Easy! Just pick the middle of the interval as x i !
Height (in.)
Frequency
xi (interval)
f i xi
60 - 62
2
61
122
63 - 65
8
64
512
66 - 68
2
67
134
69 - 71
2
70
140
72 - 74
2
73
146
SUM
16
n/a
1054
1054/16 = 65.9” (5’ 5.9”)
MODE IS THE MOST COMMON! (À LA MODE)
STEP 1 of 1: Find the one that happens most often!
Frequency of Heights (in.) of Ms. Griffith’s Homeroom
5
4
3
2
1
0
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
The mode height for the homeroom is 65” (5’ 5”).
WHAT ABOUT MODE IN GROUPS?
STEP 1/1: Find the “modal class” (happens most often).
Frequency within Homeroom Height Intervals
9
8
7
6
5
4
3
2
1
0
60 - 62
63 - 65
66 - 68
69 - 71
62 - 74
The modal class for homeroom height is 63” – 65”.
MEDIAN TELLS US THE MIDDLE!
STEP 1: Put all the data in order.
60
60
63
63
63
64
65
65
65
65
66
67
69
71
73
74
STEP 2: Find the one in the middle. If you have two, average them.
60
60
63
63
63
64
65
65
65
65
66
67
69
71
73
74
We have two: (65 + 65)/2. Our mode is 65”!
STANDARD DEVIATION
STEP 1: Enter height data into list 1.
65
67
60
63
65
63
63
64
65
73
71
66
69 -> CALC
60
74ONE-VAR STATS
Select STAT
->
(if you had a frequency 65
list, you could actually put it into
list 2, then put frequency = L2 on the stats screen)
Standard Deviation is the one that’s “baby sigma x”:
sx
TRY IT ALL QUICKLY WITH THE FREQ TABLE!
Use the calculator! X = L1, Frequency = L2!
Height
Frequency
60
2
63
3
64
1
65
4
66
1
67
1
69
1
71
1
73
1
74
1
Mean ( x )= 65.8”, Median= 65”, Mode= 65”, SD (s x)= 3.99”
EXIT SLIP: MEAN, MEDIAN, MODE AND
STANDARD DEVIATION
Misty asked Mr. Caine’s homeroom how many hours they
typically slept on a Friday night. Here were their responses:
4
8
4
9
5
9
a) Find the mean.
b) Find the median.
c) Find the mode.
6
9
6
10
6
10
7
10
7
12
8
Mean = 7.65 hours
Median = 8 hours
Technically no mode: 6, 7 and 10 all happen the most.
d) Find the standard deviation.
Standard Deviation = 2.22 hours
CUMULATIVE FREQUENCY
5 min
lesson,
7 min exit
slip
CUMULATIVE FREQUENCY SHOWS DATA
YOU HAVE ACCUMULATED THUS FAR!
Add a new column: In it, add up the frequencies so far.
Height
Frequency
Cumulative Frequency
60
2
2
63
3
5
64
1
6
65
4
10
66
1
11
67
1
12
69
1
13
71
1
14
73
1
15
74
1
16
CUMULATIVE FREQUENCY SHOWS DATA
YOU HAVE ACCUMULATED THUS FAR!
Plot the variable as x, and cumulative frequency as y.
Connect the dots with a smooth curve.
Cumulative Frequency
18
16
14
12
10
8
6
4
2
0
55
60
65
70
75
CUMULATIVE FREQUENCY SHOWS DATA
YOU HAVE ACCUMULATED THUS FAR!
Use the graph to find the 75 th percentile height.
Cumulative Frequency
18
16
14
12
10
8
6
4
2
0
0.75*16 =12
Answer:
75% of students
in Ms. Griffith’s
homeroom are
67” (5’ 7”) or
shorter.
55
60
65 67
70
75
EXIT SLIP: CUMULATIVE FREQUENCY
Misty asked Mr. Caine’s homeroom how many hours they typically
slept on a Friday night. Here were their responses in a frequency
table:
4
8
4
9
5
9
6
9
6
10
6
10
7
10
7
12
8
a) Make a cumulative frequency table.
b) Sketch a cumulative frequency graph.
c)
What is the 25 th percentile for # hours of sleep?
d) Complete this sentence using (c): 25% of students in Mr.
Caine’s homeroom typically sleep ___ hours or fewer on Friday
nights.
EXIT SLIP: CUMULATIVE FREQUENCY
Cumulative Frequency Table
Hrs Slept
Freq.
Cum. Freq.
4
2
2
5
1
3
6
3
6
7
2
8
8
2
10
9
3
13
10
3
16
12
1
17
Cumulative Frequency
18
16
14
12
10
8
6
4
2
0
0
5
10
15
25th percentile means 0.25 * 17 = 4.25 students. Follow the line!
25% of students in Mr. Caine’s homeroom typically sleep 5.5 hours or fewer on Fri. nights.
EXIT SLIP: CUMULATIVE FREQUENCY
Misty asked Mr. Caine’s homeroom how many hours they typically
slept on a Friday night. Here were their responses in a frequency
table:
4
8
4
9
5
9
6
9
6
10
6
10
7
10
7
12
8
a) Make a cumulative frequency table.
b) Sketch a cumulative frequency graph.
c)
What is the 25 th percentile for # hours of sleep?
d) Complete this sentence using (c): 25% of students in Mr.
Caine’s homeroom typically sleep ___ hours or fewer on Friday
nights.
FLASH SECTION 1:
STATISTICS VOCAB
2 min
lesson,
3 min exit
slip
MAIN VOCAB WORDS MISSED
 Discrete – Data you count, or data that has been rounded
 Examples: Shoe size, number of people, number of trees, clothes size
 Continuous – Measured data, can take more decimal places
 Examples: Height, weight, length, distance, speed
 Outlier – Data far away from the main body of data.
 Formal definition: data more than 3 std dev away from the mean
 Example: Sheldon in “Big Bang Theory” in terms of IQ
 Parameter – The variable when we’re talking about population
 Example: Average height of IDEA Donna seniors, average income of US
 Statistic – The variable when we’re talking about the sample
 Example: Average height of the 15 people I happened to ask
FLASH EXIT SLIP - VOCAB!!!
Possible answer choices:
A – Outlier
C – Statistic
B – Parameter
D – Continuous
E – Discrete
1. Height is an example of a continuous (D) variable because
I measure to get the data.
2. An outlier (A) is a datum that lies outside the standard,
middle group of data.
3. If I asked every single US resident his or her age and found
the mean, I would have a parameter (B) .
4. Shoe size is a discrete (E) variable because only certain
sizes exist.
5. If I asked a sample of Texas residents their income and
found the average, I would have a statistic (C) .
FLASH SECTION 2:
BOX PLOTS
3 min
lesson,
3 min exit
slip
BOXPLOTS 101
STEP 1: Enter data into calculator (L1) and find the quarters!
(0%, 25%, 50%, 75%, 100% …aka… min, Q1 , med, Q3, max)
60
60
65
65
63
66
63
67
63
69
64
71
65
73
65
74
Min = 60, Q1 = 63, Med = 65, Q3 = 68, Max = 74
STEP 2: Make the Boxplot: Scale, Dots, Box, Connect!
EXIT SLIP: BOX PLOTS
Misty asked Mr. Caine’s homeroom how many hours they
typically slept on a Friday night. Here were their responses in a
frequency table:
4
8
4
9
5
9
6
9
a) Find the following:
a)
b)
c)
d)
e)
Min = 4
Q1 = 6
Med = 8
Q3 = 9.5
Max = 12
6
10
6
10
7
10
7
12
8
I got to go to the
moon because I did
my stats study guide!
It made me smarter!