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

1

2

3

4

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

10

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

5

10

15

20

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!