Students practice creating frequency tables using age data from a classroom survey.

Explanation:
We are given a list of student ages, and we need to count how many students fall into each age group (4–5, 6–7, etc.), then record the frequency using tally marks and numbers.

First, let’s list all the ages clearly (they’re in one long row; I’ll break them into lines for easier counting):

10, 11, 7, 7, 15, 9, 8, 12, 4, 6, 4, 7, 11, 12, 10, 8, 9, 6, 14,
5, 9, 8, 14, 8, 7, 6, 9, 9, 10, 5, 7, 10, 12, 7, 9, 13, 11, 8, 5,
4, 7, 5, 12, 12, 13, 10, 9, 5, 6, 4, 9, 10, 11, 8, 8, 6, 9, 15,
13, 7, 14, 9, 10, 11, 5, 8, 9, 4, 5, 10, 12, 7, 8, 11, 7, 7,
8, 9, 7, 4, 6, 5, 14, 15, 9, 10, 9, 8, 7, 4, 5, 6, 10, 11, 9,
9, 10, 14

Let me count how many total numbers there are to verify:
Each line has 20 numbers, and there are 6 lines → 6 × 20 = 120 data points. Good — we’ll count frequencies totaling 120.

Now, define the age groups:

- 4–5: includes ages 4 and 5
- 6–7: includes ages 6 and 7
- 8–9: includes ages 8 and 9
- 10–11: includes ages 10 and 11
- 12–13: includes ages 12 and 13
- 14–15: includes ages 14 and 15

We’ll go through the list and tally each age.

I’ll make a table as I count:

Start with zeros:
- 4–5: 0
- 6–7: 0
- 8–9: 0
- 10–11: 0
- 12–13: 0
- 14–15: 0

Now go number by number (I’ll group mentally to speed up, but carefully):

Let’s count occurrences of each individual age first (more accurate):

Count of age 4:
Look through list:
Line 1: 4, 4 → 2
Line 2: 4 → 1
Line 3: 4, 4 → 2
Line 4: 4 → 1
Line 5: 4, 4 → 2
Line 6: 4 → 1
Also line 3: “4, 7, 5…” — already counted
Let me list all positions with 4:

From full list:
10, 11, 7, 7, 15, 9, 8, 12, 4, 6, 4, 7, ... → 2
..., 5, 9, 8, 14, 8, 7, 6, 9, 9, 10, 5, 7, 10, 12, 7, 9, 13, 11, 8, 5,
4, 7, 5, ... → 1 more (3)
..., 13, 7, 14, 9, 10, 11, 5, 8, 9, 4, 5, 10, ... → 1 more (4)
..., 8, 9, 7, 4, 6, 5, 14, 15, 9, 10, 9, 8, 7, 4, 5, 6, ... → two more (6)
Wait — let’s do systematic count using a frequency table.

Better approach: Write down all numbers and use a counter.

I’ll copy the full list and count using a tally:

Full data (120 numbers):
1.10
2.11
3.7
4.7
5.15
6.9
7.8
8.12
9.4
10.6
11.4
12.7
13.11
14.12
15.10
16.8
17.9
18.6
19.14
20.5
21.9
22.8
23.14
24.8
25.7
26.6
27.9
28.9
29.10
30.5
31.7
32.10
33.12
34.7
35.9
36.13
37.11
38.8
39.5
40.4
41.7
42.5
43.12
44.12
45.13
46.10
47.9
48.5
49.6
50.4
51.9
52.10
53.11
54.8
55.8
56.6
57.9
58.15
59.13
60.7
61.14
62.9
63.10
64.11
65.5
66.8
67.9
68.4
69.5
70.10
71.12
72.7
73.8
74.11
75.7
76.7
77.8
78.9
79.7
80.4
81.6
82.5
83.14
84.15
85.9
86.10
87.9
88.8
89.7
90.4
91.5
92.6
93.10
94.11
95.9
96.9
97.10
98.14

Wait — that’s only 98. I must have miscounted. Let me recount total entries.

Original text (copy exactly as given, split by commas):

"10, 11, 7, 7, 15, 9, 8, 12, 4, 6, 4, 7, 11, 12, 10, 8, 9, 6, 14,
5, 9, 8, 14, 8, 7, 6, 9, 9, 10, 5, 7, 10, 12, 7, 9, 13, 11, 8, 5,
4, 7, 5, 12, 12, 13, 10, 9, 5, 6, 4, 9, 10, 11, 8, 8, 6, 9, 15,
13, 7, 14, 9, 10, 11, 5, 8, 9, 4, 5, 10, 12, 7, 8, 11, 7, 7,
8, 9, 7, 4, 6, 5, 14, 15, 9, 10, 9, 8, 7, 4, 5, 6, 10, 11, 9,
9, 10, 14"

Let me count commas + 1.

I’ll paste into a counter mentally:
First line: "10, 11, 7, 7, 15, 9, 8, 12, 4, 6, 4, 7, 11, 12, 10, 8, 9, 6, 14" → that's 19 numbers
Second: "5, 9, 8, 14, 8, 7, 6, 9, 9, 10, 5, 7, 10, 12, 7, 9, 13, 11, 8, 5" → 20
Third: "4, 7, 5, 12, 12, 13, 10, 9, 5, 6, 4, 9, 10, 11, 8, 8, 6, 9, 15" → 19
Fourth: "13, 7, 14, 9, 10, 11, 5, 8, 9, 4, 5, 10, 12, 7, 8, 11, 7, 7" → 18
Fifth: "8, 9, 7, 4, 6, 5, 14, 15, 9, 10, 9, 8, 7, 4, 5, 6, 10, 11, 9" → 19
Sixth: "9, 10, 14" → 3

Total: 19+20+19+18+19+3 = 98. Hmm, but worksheet likely expects 100 or so — maybe I missed something.

Wait — look again at original block (in problem): it's one paragraph, maybe line breaks are just for formatting. Let me count all numbers in the raw string:

"10, 11, 7, 7, 15, 9, 8, 12, 4, 6, 4, 7, 11, 12, 10, 8, 9, 6, 14, 5, 9, 8, 14, 8, 7, 6, 9, 9, 10, 5, 7, 10, 12, 7, 9, 13, 11, 8, 5, 4, 7, 5, 12, 12, 13, 10, 9, 5, 6, 4, 9, 10, 11, 8, 8, 6, 9, 15, 13, 7, 14, 9, 10, 11, 5, 8, 9, 4, 5, 10, 12, 7, 8, 11, 7, 7, 8, 9, 7, 4, 6, 5, 14, 15, 9, 10, 9, 8, 7, 4, 5, 6, 10, 11, 9, 9, 10, 14"

Let me split by comma and count items:

I’ll simulate in mind:
I can instead use a reliable method: group and count frequencies directly using careful scan.

Let me tally each age from 4 to 15:

Age 4: find all 4s
Positions (just scanning):
- after 12 → 4
- then 4 again
- later: “4, 7, 5…”
- “4, 9, 10…”
- “4, 5, 10…”
- “8, 9, 7, 4…”
- “7, 4, 5…”
- “7, 4, 5…”
Let me write all 4s I see:

From list:
1. 4 (9th)
2. 4 (11th)
3. 4 (40th)
4. 4 (50th)
5. 4 (68th)
6. 4 (80th)
7. 4 (90th)
That’s 7 so far.

Wait also: in line “…8, 9, 7, 4, 6, 5…” — that’s #80
And “…7, 4, 5, 6…” — #90
And earlier: “4, 7, 5, …” is #40
Let me instead use a different strategy: I’ll write a quick frequency count manually but accurately.

I found an online-style approach: let’s sort the data mentally by ranges.

Better: I’ll count using code-like logic here.

Let me list all values in order and increment counters:

Initialize:
freq = {4:0,5:0,6:0,7:0,8:0,9:0,10:0,11:0,12:0,13:0,14:0,15:0}

Now go through each number in the given sequence (I’ll read slowly):

1. 10 → freq[10] = 1
2. 11 → 11:1
3. 7 → 7:1
4. 7 → 7:2
5. 15 → 15:1
6. 9 → 9:1
7. 8 → 8:1
8. 12 → 12:1
9. 4 → 4:1
10. 6 → 6:1
11. 4 → 4:2
12. 7 → 7:3
13. 11 → 11:2
14. 12 → 12:2
15. 10 → 10:2
16. 8 → 8:2
17. 9 → 9:2
18. 6 → 6:2
19. 14 → 14:1
20. 5 → 5:1
21. 9 → 9:3
22. 8 → 8:3
23. 14 → 14:2
24. 8 → 8:4
25. 7 → 7:4
26. 6 → 6:3
27. 9 → 9:4
28. 9 → 9:5
29. 10 → 10:3
30. 5 → 5:2
31. 7 → 7:5
32. 10 → 10:4
33. 12 → 12:3
34. 7 → 7:6
35. 9 → 9:6
36. 13 → 13:1
37. 11 → 11:3
38. 8 → 8:5
39. 5 → 5:3
40. 4 → 4:3
41. 7 → 7:7
42. 5 → 5:4
43. 12 → 12:4
44. 12 → 12:5
45. 13 → 13:2
46. 10 → 10:5
47. 9 → 9:7
48. 5 → 5:5
49. 6 → 6:4
50. 4 → 4:4
51. 9 → 9:8
52. 10 → 10:6
53. 11 → 11:4
54. 8 → 8:6
55. 8 → 8:7
56. 6 → 6:5
57. 9 → 9:9
58. 15 → 15:2
59. 13 → 13:3
60. 7 → 7:8
61. 14 → 14:3
62. 9 → 9:10
63. 10 → 10:7
64. 11 → 11:5
65. 5 → 5:6
66. 8 → 8:8
67. 9 → 9:11
68. 4 → 4:5
69. 5 → 5:7
70. 10 → 10:8
71. 12 → 12:6
72. 7 → 7:9
73. 8 → 8:9
74. 11 → 11:6
75. 7 → 7:10
76. 7 → 7:11
77. 8 → 8:10
78. 9 → 9:12
79. 7 → 7:12
80. 4 → 4:6
81. 6 → 6:6
82. 5 → 5:8
83. 14 → 14:4
84. 15 → 15:3
85. 9 → 9:13
86. 10 → 10:9
87. 9 → 9:14
88. 8 → 8:11
89. 7 → 7:13
90. 4 → 4:7
91. 5 → 5:9
92. 6 → 6:7
93. 10 → 10:10
94. 11 → 11:7
95. 9 → 9:15
96. 9 → 9:16
97. 10 → 10:11
98. 14 → 14:5

That’s 98 numbers. But maybe the original has 100 — however, worksheet likely designed with these 98. Let’s sum frequencies to verify:

4:7
5:9
→ 4–5 total = 16

6:7
7:13
→ 6–7 = 20

8:11
9:16
→ 8–9 = 27

10:11
11:7
→ 10–11 = 18

12:6
13:3
→ 12–13 = 9

14:5
15:3
→ 14–15 = 8

Now sum: 16 + 20 = 36; +27 = 63; +18 = 81; +9 = 90; +8 = 98. ✔ matches.

So frequencies are:
- 4–5: 7 + 9 = 16
- 6–7: 7 + 13 = 20
- 8–9: 11 + 16 = 27
- 10–11: 11 + 7 = 18
- 12–13: 6 + 3 = 9
- 14–15: 5 + 3 = 8

Tally marks: each group of 5 is four vertical lines and a diagonal slash.

So:
- 16 → |||| |||| |||| || (that’s 3 groups of 5 = 15, plus 1 → actually: 16 = 3×5 +1 → |||| / |||| / |||| / | ) → better written as: IIII IIII IIII I (but standard tally: groups of 5: “||||/” repeated)

Standard tally for 16:
||||/ ||||/ ||||/ | → three full groups (15) + 1

Similarly:
- 20: four groups: ||||/ ||||/ ||||/ ||||/
- 27: five groups (25) + 2 → ||||/ ×5 and ||
- 18: three groups (15) + 3 → ||||/ ||||/ ||||/ |||
- 9: one group (5) + 4 → ||||/ ||||
- 8: one group + 3 → ||||/ |||

But the question only asks to “Enter the data in the following table by tally marks and note the frequency.” So we provide frequency numbers (and optionally tallies — but final answer likely expects frequencies).

Since the table has columns: Age Group, Tally Marks, Frequency — and the instruction says “note the frequency”, the expected final output is the frequency numbers.

Thus:

4–5 → 16
6–7 → 20
8–9 → 27
10–11 → 18
12–13 → 9
14–15 → 8

Let me double-check a few counts:

Count of 9s: I had 16. Let me spot-check: in first 20 numbers: positions 6,17,21,27,28,35,38,47,51,57,62,67,78,85,95,96 → that’s 16. Yes.

Count of 7s: I had 13. Let's list 7 positions: 3,4,12,25,31,34,41,60,72,75,76,79,89 = 13. Correct.

So frequencies are solid.

Final Answer:
4–5: 16
6–7: 20
8–9: 27
10–11: 18
12–13: 9
14–15: 8