Psst … you should have started the Do Now!
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Transcript of Psst … you should have started the Do Now!
Psst… you should have started the Do Now!
STATISTICS REVIEW
COPY DOWN THIS DATA: HEIGHTS OF
MS. G’S HOMEROOM STUDENTS:
65 67 60 6365 63 63 6465 73 71 6669 60 74 65
10 min lesson,5 min exit slip
COLUMN GRAPHS,FREQUENCY TABLES,
FREQUENCY HISTOGRAMS
STEP 1: FREQUENCY TABLE (variable x, freq. y)Height Frequency60 263 364 165 466 167 169 171 173 174 1
COLUMN GRAPHS MEASURE DISCRETE DATA!
STEP 2: COLUMN GRAPH
COLUMN GRAPHS MEASURE DISCRETE DATA!
60 61 62 63 64 65 66 67 68 69 70 71 72 73 740
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5
Frequency of Heights (in.) of Ms. Grif -fith’s Homeroom
ProsSuper easy to make
Easy to read Even for middle
schoolers!
Abundantly clear
ConsCan take a long time
Hard to see trends for groups of data… (for example, is it coincidence or important that only 1 person is 64”?)
PROS AND CONS OF COLUMN GRAPHS
STEP 1: Make a Frequency Table with Intervals
FREQUENCY HISTOGRAMS MEASURE CONTINUOUS OR GROUPED DATA!
Height Interval (inches)
Frequency
60 - 62 263 - 65 866 - 68 269 - 71 272 - 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!)
STEP 2: Make a Frequency Histogram with Intervals
FREQUENCY HISTOGRAMS MEASURE CONTINUOUS OR GROUPED DATA!
60 - 62 63 - 65 66 - 68 69 - 71 72 - 7402468
10
Frequency within Homeroom Height Intervals
The bars have to be equal width and touch each other!
Column GraphsStart with freq. table
List every answer Write down frequency
Draw the column graph Bars do NOT touch Bars have equal width
Frequency HistogramsStart 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
RECAP AND COMPARE/CONTRAST
Misty asked Mr. Caine’s homeroom how many hours they typically slept on a Friday night. Here were their responses:
4 4 5 6 6 6 7 7 88 9 9 9 10 10 10 12
a) Make a frequency table for this data.
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: COLUMN GRAPHS & HISTOGRAMS
Answers are on the next slide!! (No room here)
Make a Frequency Table
Sketch a Column Graph
4 5 6 7 8 9 10 11 120
1
2
3Frequency
EXIT SLIP ANSWERS: COLUMN GRAPHS & HISTOGRAMS
(c) And (d) are on the next slide… ran out of room!
Sleep (Hours) Frequency4 25 16 37 28 29 310 312 1
Make a Frequency Table with Intervals (group)
Sketch a Frequency Histogram
4 - 5 6 - 7 8 - 9 10 - 11
12 - 13
0123456
Frequency
EXIT SLIP ANSWERS: COLUMN GRAPHS & HISTOGRAMS
Sleep Time (hours)
Frequency
4 – 5 36 – 7 58 – 9 510 – 11 312 - 13 1
8 min lesson,3 min exit slip
MEAN,MEDIAN,
MODE,STANDARD DEVIATION
MEAN MEASURES THE EXPECTED VALUE.
Add them up!
All the answers times the frequency of each answer.
Called “x-bar” – shows up as the mean on your calculator in “One-Var Stats”
Number of terms/answers
TRY OUT MEAN WITH THE FORMULA!_______
Height in inches (xi) Frequency Product (fixi)60 2 12063 3 18964 1 6465 4 26066 1 6667 1 6769 1 6971 1 7173 1 7374 1 74SUM 16 1053
1053/16 = 65.8” (5’ 5.8”)
BUT WHAT ABOUT MEAN FOR GROUPS?? ___
1054/16 = 65.9” (5’ 5.9”)
That’s Easy! Just pick the middle of the interval as x i!
Height (in.)
Frequency xi (interval)
fixi
60 - 62 2 61 12263 - 65 8 64 51266 - 68 2 67 13469 - 71 2 70 14072 - 74 2 73 146SUM 16 n/a 1054
STEP 1 of 1: Find the one that happens most often!
MODE IS THE MOST COMMON! (À LA MODE)
60 61 62 63 64 65 66 67 68 69 70 71 72 73 74012345
Frequency of Heights (in.) of Ms. Grif -fith’s Homeroom
The mode height for the homeroom is 65” (5’ 5”).
STEP 1/1: Find the “modal class” (happens most often).
WHAT ABOUT MODE IN GROUPS?
The modal class for homeroom height is 63” – 65”.60 - 62 63 - 65 66 - 68 69 - 71 62 - 74
02468
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Frequency within Homeroom Height Intervals
STEP 1: Put all the data in order.
MEDIAN TELLS US THE MIDDLE!
We have two: (65 + 65)/2. Our mode is 65”!
60 60 63 63 63 64 65 6565 65 66 67 69 71 73 74
60 60 63 63 63 64 65 6565 65 66 67 69 71 73 74
STEP 2: Find the one in the middle. If you have two, average them.
STEP 1: Enter height data into list 1.
STANDARD DEVIATION
Select STAT -> CALC -> ONE-VAR STATS(if you had a frequency 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”:
65 67 606365 63 636465 73 716669 60 7465
Use the calculator! X = L1, Frequency = L2!Height Frequency60 263 364 165 466 167 169 171 173 174 1
TRY IT ALL QUICKLY WITH THE FREQ TABLE!
Mean ( )= 65.8”, Median= 65”, Mode= 65”, SD ( )= 3.99”
Misty asked Mr. Caine’s homeroom how many hours they typically slept on a Friday night. Here were their responses:
4 4 5 6 6 6 7 7 88 9 9 9 10 10 10 12
a) Find the mean.
b) Find the median.
c) Find the mode.
d) Find the standard deviation.
EXIT SLIP: MEAN, MEDIAN, MODE AND STANDARD DEVIATION
Mean = 7.65 hours
Median = 8 hours
Technically no mode: 6, 7 and 10 all happen the most.
Standard Deviation = 2.22 hours
5 min lesson,7 min exit slip
CUMULATIVE FREQUENCY
CUMULATIVE FREQUENCY SHOWS DATA YOU HAVE ACCUMULATED THUS FAR!
Height Frequency Cumulative Frequency
60 2 263 3 564 1 665 4 1066 1 1167 1 1269 1 1371 1 1473 1 1574 1 16
Add a new column: In it, add up the frequencies so far.
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.
55 57 59 61 63 65 67 69 71 73 7502468
1012141618
Cumulative Frequency
CUMULATIVE FREQUENCY SHOWS DATA YOU HAVE ACCUMULATED THUS FAR!
Use the graph to find the 75 th percentile height.
55 57 59 61 63 65 67 69 71 73 7502468
1012141618
Cumulative Frequency
67
Answer:75% of students in Ms. Griffith’s homeroom are 67” (5’ 7”) or shorter.
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 4 5 6 6 6 7 7 88 9 9 9 10 10 10 12
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 TableHrs Slept
Freq. Cum. Freq.
4 2 25 1 36 3 67 2 88 2 109 3 1310 3 1612 1 17
EXIT SLIP: CUMULATIVE FREQUENCY
3 4 5 6 7 8 9 10 11 12 130
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Cumulative Frequency
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.
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 4 5 6 6 6 7 7 88 9 9 9 10 10 10 12
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
2 min lesson,3 min exit slip
FLASH SECTION 1:STATISTICS VOCAB
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
MAIN VOCAB WORDS MISSED
Possible answer choices:A – Outlier C – Statistic E – DiscreteB – Parameter D – Continuous
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 EXIT SLIP - VOCAB!!!
3 min lesson,3 min exit slip
FLASH SECTION 2:BOX PLOTS
STEP 1: Enter data into calculator (L1) and find the quarters!(0%, 25%, 50%, 75%, 100% …aka… min, Q1, med, Q3, max)
BOXPLOTS 101
60 60 63 63 63 64 65 6565 65 66 67 69 71 73 74
Min = 60, Q1 = 63, Med = 65, Q3 = 68, Max = 74
STEP 2: Make the Boxplot: Scale, Dots, Box, Connect!
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 4 5 6 6 6 7 7 88 9 9 9 10 10 10 12
a) Find the following:a) Min = 4b) Q1 = 6c) Med = 8d) Q3 = 9.5e) Max = 12
EXIT SLIP: BOX PLOTS
I got to go to the moon because I
did my stats study guide! It made me
smarter!