Bivariate Data Worksheets Pdf - Fill and Sign Printable Template ... - Free Printable

Let’s go through each problem one by one. I’ll solve them step by step so you can follow along easily.

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Problem 1: Apples and Mangoes

We are given data for 10 days showing how many apples and mangoes were sold. We need to describe the association — that means, do they tend to go up together? Down together? Or no pattern?

Let’s look at a few days:

- Day 1: Apple = 82, Mango = 38 → both high
- Day 5: Apple = 45, Mango = 37 → both lower
- Day 6: Apple = 55, Mango = 39 → still low
- Day 8: Apple = 76, Mango = 71 → both higher again
- Day 10: Apple = 34, Mango = 81 → apple low, mango HIGH ← this breaks the pattern!

Wait — let’s check if there’s a general trend.

Actually, let’s list them side by side:

Day | Apple | Mango
1 | 82 | 38
2 | 49 | 44
3 | 81 | 49
4 | 26 | 48
5 | 45 | 37
6 | 55 | 39
7 | 85 | 71
8 | 76 | 96 ← wait, in the table it says 96? Let me double-check the original image... Actually, looking back, Day 8 Mango is 96? But in your text above it says “Mango 38 44 49 48 37 39 71 96 83 84” — yes, Day 8 Mango is 96.

But Apple on Day 8 is 76 — which is high, and Mango is 96 — also very high.

Day 9: Apple 97, Mango 83 → both high
Day 10: Apple 34, Mango 81 → Apple low, Mango high ← outlier?

Actually, let’s see: when Apple is high (like Day 1, 3, 7, 8, 9), Mango is often medium to high. When Apple is low (Day 4, 5, 6, 10), Mango varies — sometimes medium, sometimes high.

There’s no clear strong positive or negative association. For example:

- High Apple + Low Mango? Not really.
- Low Apple + High Mango? Sometimes (Day 10).
- High Apple + High Mango? Yes (Days 7,8,9)
- Low Apple + Low Mango? Day 5: Apple 45, Mango 37 — kinda low

Actually, let’s calculate roughly: most of the time, when Apple goes up, Mango tends to go up too — except Day 10.

But Day 10 might be an exception. Overall, there seems to be a positive association — as apple sales increase, mango sales tend to increase too, with maybe one or two exceptions.

✔ Final answer for #1: There is a positive association between apple and mango sales — when more apples are sold, more mangoes tend to be sold too.

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Problem 2: Books and Pens

Student | Books | Pens
1 | 35 | 47
2 | 20 | 71
3 | 28 | 55
4 | 60 | 55
5 | 40 | 63
6 | 48 | 12 ← big drop!
7 | 40 | 87
8 | 49 | 74
9 | 49 | 96
10 | 30 | 46

Look at Student 6: bought 48 books but only 12 pens — that’s unusual.

Student 2: 20 books, 71 pens — lots of pens, few books.

Student 9: 49 books, 96 pens — lots of both.

Is there a pattern? Let’s see:

When books are low (Students 2, 3, 10), pens vary: 71, 55, 46 — not consistent.

When books are high (Students 4, 5, 7, 8, 9), pens are mostly high — except Student 6 (only 12 pens).

So overall, except for Student 6, when students buy more books, they also tend to buy more pens.

That suggests a positive association, even though there’s one outlier.

✔ Final answer for #2: There is a positive association — students who buy more books usually buy more pens too, with one exception (Student 6).

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Problem 3: Men and Women at College Game

Year | Man | Woman
1 | 22 | 22
2 | 47 | 58
3 | 84 | 61
4 | 12 | 53
5 | 26 | 43
6 | 33 | 81
7 | 44 | 86
8 | 54 | 94
9 | 71 | 50
10 | 68 | 54

Check trends:

Year 1: equal
Year 2: men 47, women 58 → women more
Year 3: men 84, women 61 → men more
Year 4: men 12, women 53 → women much more
Year 5: men 26, women 43 → women more
Year 6: men 33, women 81 → women way more
Year 7: men 44, women 86 → women more
Year 8: men 54, women 94 → women more
Year 9: men 71, women 50 → men more
Year 10: men 68, women 54 → men more

So in early years (1–5), mixed. Later years (6–8), women dominate. Then Years 9–10, men catch up.

No clear consistent pattern. Sometimes men > women, sometimes women > men.

In fact, let’s count:

Years where women > men: 2,3?, wait Year 3: men 84 > women 61 → men win
Actually:

Women > men: Year 2 (58>47), Year 4 (53>12), Year 5 (43>26), Year 6 (81>33), Year 7 (86>44), Year 8 (94>54) → that’s 6 years

Men > women: Year 3 (84>61), Year 9 (71>50), Year 10 (68>54) → 3 years

Equal: Year 1

So mostly, women attended more than men — especially in middle years.

But is there an *association*? That would mean: as men increase, do women increase? Or decrease?

Let’s see:

From Year 1 to 3: men go 22→47→84 (up), women go 22→58→61 (up) → positive

Year 4: men crash to 12, women jump to 53 → opposite

Year 5: men 26, women 43 → both up from previous? Men up from 12, women down from 53? Not clear.

Actually, plot mentally: no steady line. Some years both up, some years one up one down.

Best description: No clear association — attendance of men and women doesn’t consistently rise or fall together. Sometimes both increase, sometimes one increases while the other decreases.

✔ Final answer for #3: There is no clear association between the number of men and women attending — their numbers don’t consistently move together.

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Problem 4: Pizza and Burger Orders

Student | Pizza | Burger
1 | 34 | 40
2 | 69 | 28
3 | 42 | 37
4 | 12 | 57
5 | 22 | 85
6 | 54 | 78
7 | 86 | 34
8 | 29 | 47
9 | 54 | 76
10 | 37 | 50

Look for patterns:

Student 1: Pizza 34, Burger 40 → similar
Student 2: Pizza 69 (high), Burger 28 (low) ← inverse
Student 3: Pizza 42, Burger 37 → similar
Student 4: Pizza 12 (low), Burger 57 (high) ← inverse
Student 5: Pizza 22 (low), Burger 85 (very high) ← inverse
Student 6: Pizza 54, Burger 78 → both high? Wait, 54 and 78 — burger higher
Student 7: Pizza 86 (very high), Burger 34 (low) ← inverse
Student 8: Pizza 29, Burger 47 → burger higher
Student 9: Pizza 54, Burger 76 → burger higher
Student 10: Pizza 37, Burger 50 → burger higher

Notice: whenever pizza is HIGH, burger is LOW (Students 2, 7)
Whenever pizza is LOW, burger is HIGH (Students 4, 5)

Even Student 6: Pizza 54 (medium-high), Burger 78 (high) — not inverse, but close.

Student 1,3: medium-medium — neutral.

This looks like a negative association — when pizza orders go up, burger orders tend to go down, and vice versa.

Why? Maybe students choose one or the other — not both.

✔ Final answer for #4: There is a negative association — students who order more pizza tend to order fewer burgers, and those who order less pizza tend to order more burgers.

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Final Answers:

1. Positive association between apple and mango sales.
2. Positive association between books and pens purchased.
3. No clear association between men and women attending the game.
4. Negative association between pizza and burger orders.