1. 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

2. 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

4. Frequency Distribution Histogram Class Boundaries are widths of bars Class Heights are the Frequencies of each class Frequency # of subscribers Internet usage

5. Frequency Distribution Polygons Midpoints of classes are x-values :extend ends Frequencies of classes are y-values: ends at 0 Connect points (line graph) Time online in minutes (midpoints) Frequency (# of subscribers)

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

7. Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) USE 6 Classes - Width (63-0)/6=10.5 ≈ 11 ClassClass Bound. TallyFreq.Mid. Pt.Rel. Freq. Cum. Freq. 0 11 22 33 44 55

8. Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) USE 6 Classes - Width (63-0)/6=10.5 ≈ 11 ClassClass Bound. TallyFreq.Mid. Pt.Rel. Freq. Cum. Freq. 0-10 11-21 22-32 33-43 44-54 55-65

9. Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) USE 6 Classes - Width (63-0)/6=10.5 ≈ 11 ClassClass Bound. TallyFreq.Mid. Pt.Rel. Freq. Cum. Freq. 0-10-.5-10.5 11-2110.5-21.5 22-3221.5-32.5 33-4332.5-43.5 44-5443.5-54.5 55-6554.5-65.5

10. Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) USE 6 Classes - Width (63-0)/6=10.5 ≈ 11 ClassClass Bound. TallyFreq.Mid. Pt.Rel. Freq. Cum. Freq. 0-10-.5-10.55 11-2110.5-21.516 22-3221.5-32.527 33-4332.5-43.538 44-5443.5-54.549 55-6554.5-65.560

11. Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) USE 6 Classes - Width (63-0)/6=10.5 ≈ 11 ClassClass Bound. TallyFreqMid. Pt.Rel. Freq. Cum. Freq. 0-10-.5-10.5IIII IIII IIII IIII IIII II 275 11-2110.5-21.5IIII IIII III1316 22-3221.5-32.5IIII IIII IIII I 1627 33-4332.5-43.5IIII II738 44-5443.5-54.5IIII IIII I1149 55-6554.5-65.5III360 77

12. Example: Do Try it Yourself p. 35 # 3 & 4 (Use data on p. 29) USE 6 Classes - Width (63-0)/6=10.5 ≈ 11 ClassClass Bound. TallyFreqMid. Pt.Rel. Freq. Cum. Freq. 0-10-.5-10.5IIII IIII IIII IIII IIII II 275.350624 11-2110.5-21.5IIII IIII III1316.168840 22-3221.5-32.5IIII IIII IIII I 1627.207856 33-4332.5-43.5IIII II738.090963 44-5443.5-54.5IIII IIII I1149.142974 55-6554.5-65.5III360.039077

13. Histogram Frequency 5 16 27 38 49 60

14. Frequency Polygon Frequency