QUESTION IMAGE
Question
challenge you ask 170 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.
construct the two - way frequency table.
how do you feel about a longer school year?
Step1: Fill 6th Graders' Very Unhappy
Total 6th Graders = 51. Sum known 6th graders: $8 + 18 + 12 = 38$. So Very Unhappy = $51 - 38 = 13$.
Step2: Fill 7th Graders' Total
Total students = 170. Sum known totals: $51 + 43 = 94$. So 7th Graders Total = $170 - 94 = 76$.
Step3: Fill 7th Graders' Neutral
Total Neutral = 38. Sum known Neutral: $18 + 8 = 26$. So 7th Neutral = $38 - 26 = 12$.
Step4: Fill 7th Graders' Happy
Total Happy = 25. Sum known Happy: $1 = 1$. Let 6th Happy = $x$, 7th Happy = $y$. $x + y + 1 = 25$ → $x + y = 24$. Total 7th: $23 + 11 + 12 + y + 15 = 76$ → $61 + y =76$ → $y=15$. So 6th Happy = $24 -15=9$.
Step5: Fill 8th Graders' Very Unhappy
Total Very Unhappy =38. Sum known Very Unhappy: $13 +23=36$. So 8th Very Unhappy = $38 -36=2$.
Step6: Fill 8th Graders' Unhappy Total
Total Unhappy = $8 +11 +10=29$.
Step7: Fill 8th Graders' Very Happy Total
Total Very Happy = $12 +15 + (43 - (2+10+8+1))=12+15+22=49$.
Step8: Combine Dislike (Very Unhappy + Unhappy) and Like (Neutral + Happy + Very Happy)
Dislike: $38 +29=67$; Like: $38 +25 +49=112$. By grade: 6th Dislike=$13+8=21$, 6th Like=$18+9+12=39$; 7th Dislike=$23+11=34$,7th Like=$12+15+15=42$;8th Dislike=$2+10=12$,8th Like=$8+1+22=31$.
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Original two-way frequency table (filled):
| Grade | 6th Graders | 7th Graders | 8th Graders | Total |
|---|---|---|---|---|
| Unhappy | 8 | 11 | 10 | 29 |
| Neutral | 18 | 12 | 8 | 38 |
| Happy | 9 | 15 | 1 | 25 |
| Very Happy | 12 | 15 | 22 | 49 |
| Total | 51 | 76 | 43 | 170 |
New two-way frequency table (Dislike/Like):
| Grade | 6th Graders | 7th Graders | 8th Graders | Total |
|---|---|---|---|---|
| Like | 39 | 42 | 31 | 112 |
| Total | 51 | 76 | 43 | 170 |