Math worksheet focusing on statistical measures: mean, median, mode, and range.

Let’s go step by step to solve this worksheet.

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Part 1: Use the word bank for each definition

Word Bank:
Data Set, Mean, Median, Mode, Range

We match each definition to the correct term:

1. The number that appears most often in a set of data.
→ That’s the Mode.

2. The number of a set of data that is often referred to as the average.
→ That’s the Mean.

3. The difference between the lowest and highest number in a set of data.
→ That’s the Range.

4. A collection of information, usually numbers, related to a specific area of study.
→ That’s a Data Set.

5. The number located in the middle of a set of numbers when arranged from high to low.
→ Actually, it should be “arranged from low to high” — but either way, the middle number is the Median.

✔ So answers for 1–5:
1. Mode
2. Mean
3. Range
4. Data Set
5. Median

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Part 2: Answer True or False

6. The mean, median, and mode value can have the same values.
→ TRUE. Example: {2, 2, 2} → mean=2, median=2, mode=2.

7. To find range, subtract the largest number from the smallest number.
→ FALSE. You subtract the *smallest* from the *largest*. (Largest – Smallest)

8. It is possible for a set of data not to have a mode.
→ TRUE. If all numbers appear only once, there is no mode.

9. Every set of data will have a mean and median, and sometimes a mode.
→ TRUE. Mean and median always exist (you can always add and divide, or find the middle). Mode may not exist.

10. A data set must contain at least five numbers.
→ FALSE. A data set can have just one number! Like {5}.

✔ Answers for 6–10:
6. True
7. False
8. True
9. True
10. False

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Part 3: Complete the Chart

We need to calculate for each row (A to J):

- Mean: Add all numbers, divide by how many numbers.
- Median: Sort the numbers, pick the middle one (if even count, average the two middle ones).
- Mode: Number that appears most often (if none, write “none”).
- Range: Largest – Smallest.

Let’s do them one by one carefully.

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#### Row A: 68, 54, 10, 14, 81, 25, 34, 50, 37, 15, 56, 84

Count = 12 numbers

Sort: 10, 14, 15, 25, 34, 37, 50, 54, 56, 68, 81, 84

Mean: Sum = let’s add:

10+14=24; +15=39; +25=64; +34=98; +37=135; +50=185; +54=239; +56=295; +68=363; +81=444; +84=528

Sum = 528 → Mean = 528 ÷ 12 = 44

Median: 12 numbers → average of 6th and 7th: 37 and 50 → (37+50)/2 = 43.5

Mode: All numbers appear once → none

Range: 84 - 10 = 74

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#### Row B: 17, 14, 32, 67, 48, 65, 49, 67, 36, 65

Count = 10

Sort: 14, 17, 32, 36, 48, 49, 65, 65, 67, 67

Sum: 14+17=31; +32=63; +36=99; +48=147; +49=196; +65=261; +65=326; +67=393; +67=460

Mean = 460 ÷ 10 = 46

Median: 5th and 6th: 48 and 49 → (48+49)/2 = 48.5

Mode: 65 and 67 both appear twice → 65, 67 (bimodal)

Range: 67 - 14 = 53

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#### Row C: 28, 23, 68, 82, 59, 69, 24, 12, 23, 26, 48

Count = 11

Sort: 12, 23, 23, 24, 26, 28, 48, 59, 68, 69, 82

Sum: 12+23=35; +23=58; +24=82; +26=108; +28=136; +48=184; +59=243; +68=311; +69=380; +82=462

Mean = 462 ÷ 11 = 42

Median: 6th number → 28

Mode: 23 appears twice → 23

Range: 82 - 12 = 70

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#### Row D: 97, 82, 72, 75, 81, 73, 8

Count = 7

Sort: 8, 72, 73, 75, 81, 82, 97

Sum: 8+72=80; +73=153; +75=228; +81=309; +82=391; +97=488

Mean = 488 ÷ 7 ≈ 69.714... Let’s keep as fraction or round? Since others are whole, maybe check again.

Wait: 8+72=80; 80+73=153; 153+75=228; 228+81=309; 309+82=391; 391+97=488 → yes.

488 ÷ 7 = 69.714... But perhaps we leave as decimal? Or maybe I made mistake?

Actually, let’s double-check sum:

97 + 82 = 179
179 + 72 = 251
251 + 75 = 326
326 + 81 = 407
407 + 73 = 480
480 + 8 = 488 → correct.

So Mean = 488/7 ≈ 69.7 (we’ll use one decimal if needed, but let’s see other rows — some might be exact. For now, we’ll write 69.7 or 488/7? Better to compute exactly.)

But since problem doesn’t specify, and others are integers, maybe I miscalculated? No, it’s correct. We’ll write 69.7 (rounded to nearest tenth).

Actually, let’s hold off — maybe later we can recheck. For now, proceed.

Median: 4th number → 75

Mode: all unique → none

Range: 97 - 8 = 89

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#### Row E: 37, 46, 48, 68, 70, 47, 66, 42

Count = 8

Sort: 37, 42, 46, 47, 48, 66, 68, 70

Sum: 37+42=79; +46=125; +47=172; +48=220; +66=286; +68=354; +70=424

Mean = 424 ÷ 8 = 53

Median: 4th and 5th: 47 and 48 → (47+48)/2 = 47.5

Mode: all unique → none

Range: 70 - 37 = 33

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#### Row F: 77, 79, 18, 43, 84, 50, 89

Count = 7

Sort: 18, 43, 50, 77, 79, 84, 89

Sum: 18+43=61; +50=111; +77=188; +79=267; +84=351; +89=440

Mean = 440 ÷ 7 ≈ 62.857... → 62.9 (or 62.86? Let’s say 62.9)

Actually, 440 ÷ 7 = 62.857... so 62.9 rounded.

Median: 4th → 77

Mode: none → none

Range: 89 - 18 = 71

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#### Row G: 77, 99, 15, 68, 68, 56, 94, 35, 16, 27, 84, 93

Count = 12

Sort: 15, 16, 27, 35, 56, 68, 68, 77, 84, 93, 94, 99

Sum: Let’s add:

15+16=31; +27=58; +35=93; +56=149; +68=217; +68=285; +77=362; +84=446; +93=539; +94=633; +99=732

Mean = 732 ÷ 12 = 61

Median: 6th and 7th: 68 and 68 → (68+68)/2 = 68

Mode: 68 appears twice → 68

Range: 99 - 15 = 84

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#### Row H: 98, 24, 31, 21, 14, 23, 46, 65, 54, 76, 43

Count = 11

Sort: 14, 21, 23, 24, 31, 43, 46, 54, 65, 76, 98

Sum: 14+21=35; +23=58; +24=82; +31=113; +43=156; +46=202; +54=256; +65=321; +76=397; +98=495

Mean = 495 ÷ 11 = 45

Median: 6th → 43

Mode: all unique → none

Range: 98 - 14 = 84

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#### Row I: 20, 54, 11, 26, 51, 78, 42, 74, 47, 79

Count = 10

Sort: 11, 20, 26, 42, 47, 51, 54, 74, 78, 79

Sum: 11+20=31; +26=57; +42=99; +47=146; +51=197; +54=251; +74=325; +78=403; +79=482

Mean = 482 ÷ 10 = 48.2

Median: 5th and 6th: 47 and 51 → (47+51)/2 = 49

Mode: none → none

Range: 79 - 11 = 68

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#### Row J: 68, 48, 14, 23, 17, 65, 99, 29, 51

Count = 9

Sort: 14, 17, 23, 29, 48, 51, 65, 68, 99

Sum: 14+17=31; +23=54; +29=83; +48=131; +51=182; +65=247; +68=315; +99=414

Mean = 414 ÷ 9 = 46

Median: 5th → 48

Mode: none → none

Range: 99 - 14 = 85

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Now let’s compile all results into the chart.

Note: For means that are decimals, we’ll write them as decimals (to one place if needed).

Final Chart:

| | Data Set | Mean | Median | Mode | Range |
|---|-----------------------------------------------|---------|---------|----------|-------|
| A | 68,54,10,14,81,25,34,50,37,15,56,84 | 44 | 43.5 | none | 74 |
| B | 17,14,32,67,48,65,49,67,36,65 | 46 | 48.5 | 65,67 | 53 |
| C | 28,23,68,82,59,69,24,12,23,26,48 | 42 | 28 | 23 | 70 |
| D | 97,82,72,75,81,73,8 | 69.7 | 75 | none | 89 |
| E | 37,46,48,68,70,47,66,42 | 53 | 47.5 | none | 33 |
| F | 77,79,18,43,84,50,89 | 62.9 | 77 | none | 71 |
| G | 77,99,15,68,68,56,94,35,16,27,84,93 | 61 | 68 | 68 | 84 |
| H | 98,24,31,21,14,23,46,65,54,76,43 | 45 | 43 | none | 84 |
| I | 20,54,11,26,51,78,42,74,47,79 | 48.2 | 49 | none | 68 |
| J | 68,48,14,23,17,65,99,29,51 | 46 | 48 | none | 85 |

Wait — for Row D, mean was 488/7 = 69.714... which is approximately 69.7. Similarly, Row F: 440/7 ≈ 62.857 → 62.9. Row I: 48.2 is exact.

But let me double-check Row D sum again because 69.7 seems odd compared to others.

Row D: 97,82,72,75,81,73,8

Add: 97+82=179; 179+72=251; 251+75=326; 326+81=407; 407+73=480; 480+8=488 → yes.

488 ÷ 7 = 69.7142857... So 69.7 is fine.

Similarly, Row F: 77+79=156; +18=174; +43=217; +84=301; +50=351; +89=440 → 440÷7≈62.857→62.9

Okay.

Also, for Row B, mode is bimodal: 65 and 67. We write "65,67" or "65 and 67"? In charts, usually list both.

Same for others.

Now, let’s present final answers clearly.

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Final Answer:

Part 1: Definitions
1. Mode
2. Mean
3. Range
4. Data Set
5. Median

Part 2: True or False
6. True
7. False
8. True
9. True
10. False

Part 3: Completed Chart

| | Mean | Median | Mode | Range |
|---|---------|---------|----------|-------|
| A | 44 | 43.5 | none | 74 |
| B | 46 | 48.5 | 65, 67 | 53 |
| C | 42 | 28 | 23 | 70 |
| D | 69.7 | 75 | none | 89 |
| E | 53 | 47.5 | none | 33 |
| F | 62.9 | 77 | none | 71 |
| G | 61 | 68 | 68 | 84 |
| H | 45 | 43 | none | 84 |
| I | 48.2 | 49 | none | 68 |
| J | 46 | 48 | none | 85 |

(Note: Means for D, F, I are rounded to one decimal place.)