Graphs of Frequency Distributions 1 Frequency Histograms BAR

Graphs of Frequency Distributions • 1) Frequency Histograms: BAR GRAPHS – Horizontal scale quantitative: measures data values – Vertical scale: measures FREQUENCIES of classes – Consecutive bars must TOUCH • 2) Frequency Polygons: LINE GRAPHS – Line Graph: shows continuous change in frequencies – Horizontal & Vertical scales same as Histograms

Class Boundaries • Used in HISTOGRAMS • 1) Find the UPPER limit of FIRST class and LOWER limit of second class • 2) Subtract these values (Usually 1) • 3) Divide by 2 (Usually. 5) • 4) SUBTRACT this # from each lower limit and ADD this # to each upper limit: = boundaries

Frequency Distribution Histogram • Class Boundaries are widths of bars • Class Heights are the Frequencies of each class Internet usage 15 6. 5 -18. 5 min 18. 5 -30. 5 min 10 Frequency # of subscribers 5 0 30. 5 -42. 5 min 42. 5 -54. 5 min 54. 5 -66. 5 min Time online in minutes 66. 5 -78. 5 min

Frequency Distribution Polygons • Midpoints of classes are x-values : extend ends • Frequencies of classes are y-values: ends at 0 • Connect points (line graph) Internet usage 15 10 Frequency (# of subscribers) 5 Internet usage Time online in minutes (midpoints) 96, 5 84, 5 72, 5 60, 5 48, 5 36, 5 24, 5 12, 5 0

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes Class Bound. Tally Freq. Mid. Pt. Rel. Freq. Cum. Freq.

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes - Width (63 -0)/6=10. 5 ≈ 11 Class 0 11 22 33 44 55 Class Bound. Tally Freq. Mid. Pt. Rel. Freq. Cum. Freq.

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes - Width (63 -0)/6=10. 5 ≈ 11 Class 0 -10 11 -21 22 -32 33 -43 44 -54 55 -65 Class Bound. Tally Freq. Mid. Pt. Rel. Freq. Cum. Freq.

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes - Width (63 -0)/6=10. 5 ≈ 11 Class Bound. 0 -10 -. 5 -10. 5 11 -21 10. 5 -21. 5 22 -32 21. 5 -32. 5 33 -43 32. 5 -43. 5 44 -54 43. 5 -54. 5 55 -65 54. 5 -65. 5 Tally Freq. Mid. Pt. Rel. Freq. Cum. Freq.

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes - Width (63 -0)/6=10. 5 ≈ 11 Class Bound. Tally Freq. Mid. Pt. 0 -10 -. 5 -10. 5 5 11 -21 10. 5 -21. 5 16 22 -32 21. 5 -32. 5 27 33 -43 32. 5 -43. 5 38 44 -54 43. 5 -54. 5 49 55 -65 54. 5 -65. 5 60 Rel. Freq. Cum. Freq.

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes - Width (63 -0)/6=10. 5 ≈ 11 Class Bound. Tally Freq Mid. Pt. 0 -10 -. 5 -10. 5 IIII IIII II 27 5 11 -21 10. 5 -21. 5 IIII III 13 16 22 -32 21. 5 -32. 5 IIII I 16 27 33 -43 32. 5 -43. 5 IIII II 7 38 44 -54 43. 5 -54. 5 IIII I 11 49 55 -65 54. 5 -65. 5 III 3 60 77 Rel. Freq. Cum. Freq.

Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) • USE 6 Classes - Width (63 -0)/6=10. 5 ≈ 11 Class Bound. Tally Freq Mid. Pt. Rel. Freq. Cum. Freq. 0 -10 -. 5 -10. 5 IIII IIII II 27 5 . 3506 24 11 -21 10. 5 -21. 5 IIII III 13 16 . 1688 40 22 -32 21. 5 -32. 5 IIII I 16 27 . 2078 56 33 -43 32. 5 -43. 5 IIII II 7 38 . 0909 63 44 -54 43. 5 -54. 5 IIII I 11 49 . 1429 74 55 -65 54. 5 -65. 5 III 3 60 . 0390 77 77

Histogram 30 25 __-. 5 -10. 5 20 10. 5 -21. 5 -32. 5 Frequency 15 32. 5 -43. 5 10 43. 5 -54. 5 -65. 5 5 0 Ages 5 16 27 38 49 60

Frequency Polygon Ages of residents of Akhiok Alaska 30 25 20 Frequency 15 Ages of residents of Akhiok Alaska 10 5 0 -6 5 16 27 38 49 60 71