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Psst … you should have started the Do Now!

STATISTICS REVIEW copy down this data : heights of Ms. G’s homeroom students: 65 67 60 63 65 63 63 64 65 73 71 66 69 60 74 65. Psst … you should have started the Do Now!. Column graphs, frequency tableS , Frequency histograms. 10 min lesson, 5 min exit slip.

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Psst … you should have started the Do Now!

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  1. STATISTICS REVIEWcopy down this data: heights of Ms. G’s homeroom students:65 67 60 6365 6363 6465 73 71 6669 60 74 65 Psst… you should have started the Do Now!

  2. Column graphs,frequency tableS,Frequency histograms 10 min lesson, 5 min exit slip

  3. Column graphs measure discrete data! STEP 1: FREQUENCY TABLE (variable x, freq. y)

  4. Column graphs measure discrete data! STEP 2: COLUMN GRAPH

  5. PROS and CONS of column graphs Pros Cons Can 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”?) • Super easy to make • Easy to read • Even for middle schoolers! • Abundantly clear

  6. Frequency histograms measure continuous OR GROUPED data! STEP 1: Make a Frequency Table with Intervals 5 is the ideal number of intervals! The intervals have to be equal in size! (Here, I have five intervals with 3 in. each!)

  7. Frequency histograms measure continuous OR GROUPED data! STEP 2: Make a Frequency Histogram with Intervals The bars have to be equal width and touch each other!

  8. RECAP and Compare/contrast Column Graphs 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 • Start with freq. table • List every answer • Write down frequency • Draw the column graph • Bars do NOT touch • Bars have equal width

  9. 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 4 5 6 6 6 7 7 8 8 9 9 9 10 10 10 12 • Make a frequency table for this data. • Sketch a column graph for this data. • Make a frequency table with intervals of 2 hours each (e.g., 4-5 hours) for this data. • Sketch a frequency histogram for this data. Answers are on the next slide!! (No room here)

  10. EXIT SLIP ANSWERS: COLUMN GRAPHS & HISTOGRAMS Make a Frequency Table Sketch a Column Graph (c) And (d) are on the next slide… ran out of room!

  11. EXIT SLIP ANSWERS: COLUMN GRAPHS & HISTOGRAMS Make a Frequency Table with Intervals (group) Sketch a Frequency Histogram

  12. MEAN,Median,Mode,standard deviation 8 min lesson, 3 min exit slip

  13. 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

  14. TRY OUT MEAN with the formula! _______ 1053/16 = 65.8” (5’ 5.8”)

  15. But what about MEAN for groups?? ___ That’s Easy! Just pick the middle of the interval as xi! 1054/16 = 65.9” (5’ 5.9”)

  16. MODE is the most common! (à la mode) STEP 1 of 1: Find the one that happens most often! The mode height for the homeroom is 65” (5’ 5”).

  17. What about mode in groups? STEP 1/1: Find the “modal class” (happens most often). The modal class for homeroom height is 63” – 65”.

  18. Median tells us the middle! STEP 1: Put all the data in order. We have two: (65 + 65)/2. Our mode is 65”! 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 60 60 63 63 63 64 65 65 65 65 66 67 69 71 73 74

  19. STANDARD DEVIATION STEP 1: Enter height data into list 1. 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 60 6365 63 63 6465 73 71 6669 60 74 65

  20. Try it all quickly with the Freq table! Use the calculator! X = L1, Frequency = L2! Mean ( )= 65.8”, Median= 65”, Mode= 65”, SD ( )= 3.99”

  21. 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 4 5 6 6 6 7 7 8 8 9 9 9 10 10 10 12 • Find the mean. • Find the median. • Find the mode. • Find the 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

  22. Cumulative frequency 5 min lesson, 7 min exit slip

  23. Cumulative frequency shows data you have accumulated thus far! Add a new column: In it, add up the frequencies so far.

  24. 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.

  25. Cumulative frequency shows data you have accumulated thus far! Use the graph to find the 75th percentile height. Answer: 75% of students in Ms. Griffith’s homeroom are 67” (5’ 7”) or shorter. 67

  26. 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 4 5 6 6 6 7 7 8 8 9 9 9 10 10 10 12 • Make a cumulative frequency table. • Sketch a cumulative frequency graph. • What is the 25th percentile for # hours of sleep? • Complete this sentence using (c): 25% of students in Mr. Caine’s homeroom typically sleep ___ hours or fewer on Friday nights.

  27. EXIT SLIP: Cumulative frequency Cumulative Frequency Table 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.

  28. 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 4 5 6 6 6 7 7 8 8 9 9 9 10 10 10 12 • Make a cumulative frequency table. • Sketch a cumulative frequency graph. • What is the 25th percentile for # hours of sleep? • Complete this sentence using (c): 25% of students in Mr. Caine’s homeroom typically sleep ___ hours or fewer on Friday nights.

  29. Flash Section 1:Statistics vocab 2 min lesson, 3 min exit slip

  30. 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 stddev 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

  31. FLASH EXIT SLIP - VOCAB!!! Possible answer choices: A – Outlier C – Statistic E – Discrete B – Parameter D – Continuous • Height is an example of a continuous (D) variable because I measure to get the data. • An outlier (A) is a datum that lies outside the standard, middle group of data. • If I asked every single US resident his or her age and found the mean, I would have a parameter (B) . • Shoe size is a discrete (E) variable because only certain sizes exist. • If I asked a sample of Texas residents their income and found the average, I would have a statistic (C) .

  32. Flash Section 2:Box plots 3 min lesson, 3 min exit slip

  33. 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 63 63 63 64 65 65 65 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!

  34. 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 4 5 6 6 6 7 7 8 8 9 9 9 10 10 10 12 • Find the following: • Min =4 • Q1 = 6 • Med = 8 • Q3 = 9.5 • Max = 12

  35. I got to go to the moon because I did my stats study guide! It made me smarter!

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