Question

challenge you ask 215 of your classmates how they feel about the school year being made longer. complete the two - way frequency table to show the results of the survey. use pencil and paper. combine the very unhappy and unhappy categories into one category called dislike and combine the happy and very happy categories into one category called like. complete a new two - way frequency table.
how do you feel about a longer school year?
construct the two - way frequency table.

Explanation:

Step1: Fill 6th graders' Very Unhappy

Total 6th graders = 77. Sum of known 6th graders: 24 (Unhappy) + 2 (Neutral) + 8 (Very Happy) = 34. So Very Unhappy 6th graders = 77 - 34 = 43.

Step2: Fill 7th graders' Neutral

Total 7th graders = 91. Sum of known 7th graders: 23 (Very Unhappy) + 20 (Unhappy) + 9 (Very Happy) = 52. So Neutral 7th graders = 91 - 52 = 39.

Step3: Fill 7th graders' Happy

Total 7th graders = 91. Sum of known 7th graders: 23 + 20 + 39 + 9 = 91. So Happy 7th graders = 91 - 91 = 0.

Step4: Fill 8th graders' Very Unhappy

Total Very Unhappy = 48. Sum of known Very Unhappy: 43 (6th) + 23 (7th) = 66? Wait correction: 6th Very Unhappy is 77 - (24+2+8) = 43. Total Very Unhappy row is 48, so 8th Very Unhappy = 48 - 43 -23 = -18? No mistake: 6th total is 77: Very Unhappy (V) + Unhappy(24)+Neutral(2)+Happy(H)+Very Happy(8)=77 → V+H=77-34=43. 7th total 91: 23+20+N+0+9=91 → N=39. 8th total 47: V+2+15+14+VH=47 → V+VH=47-31=16. Total Unhappy row: 24+20+2=46. Total Neutral row: 2+39+15=56. Total Happy row: H+0+14=65 → H=51. Then 6th V=43-51=-8? Incorrect initial assumption: Let's use total 215. 6th(77)+7th(91)+8th(47)=215 correct. Total Very Happy:8+9+VH=? Total Unhappy row:24+20+2=46. Total Neutral:2+N+15=26 → N=9 (7th Neutral=9). 7th total:23+20+9+H+9=91 → H=91-61=30. 6th Happy: total Happy=65=H6+30+14 → H6=21. 6th Very Unhappy:77-21-24-2-8=22. 8th Very Unhappy:48-22-23=3. 8th Very Happy:47-3-2-15-14=13. Total Very Happy:8+9+13=30. Total row:48+46+26+65+30=215 correct.

Step5: Combine Dislike (Very Unhappy+Unhappy) and Like (Neutral+Happy+Very Happy)

Dislike: 48+46=94; Like:26+65+30=121. By grade: 6th Dislike=22+24=46; 6th Like=2+21+8=31. 7th Dislike=23+20=43;7th Like=9+30+9=48. 8th Dislike=3+2=5;8th Like=15+14+13=42.

Answer:

Original Completed Table:

Grade	6th Graders	7th Graders	8th Graders	Total
Unhappy	24	20	2	46
Neutral	2	9	15	26
Happy	21	30	14	65
Very Happy	8	9	13	30
Total	77	91	47	215

New Two-way Table (Dislike vs Like):

Grade	Dislike	Like	Total
7th	43	48	91
8th	5	42	47
Total	94	121	215