Question

consider the following data set.
the heights (rounded to the nearest inch) of 30 students are given.
68 66 72 65 67 69 70 63 63 67
69 63 69 65 71 63 64 69 69 63
67 65 66 69 63 68 67 71 70 66
prepare a frequency distribution for the data set.
height frequency
63
64
65
66
67
68
69
70
71
72

Explanation:

Step1: Count frequency of 63

Look at the data: 63 appears at positions (indexes start at 1): 8,9,12,14,19,25. So count: 6 times.

Step2: Count frequency of 64

64 appears at position 15. Count: 1 time.

Step3: Count frequency of 65

65 appears at positions 4,13,22. Count: 3 times.

Step4: Count frequency of 66

66 appears at positions 2,23,29. Count: 3 times.

Step5: Count frequency of 67

67 appears at positions 5,10,21,26. Count: 4 times.

Step6: Count frequency of 68

68 appears at positions 1,24. Count: 2 times.

Step7: Count frequency of 69

69 appears at positions 6,11,13? Wait, recheck: positions 6 (69),11 (69),16 (69),17 (69),20 (69),27 (69). Wait original data: first row: 68,66,72,65,67,69,70,63,63,67 (so 69 at 6th). Second row:69,63,69,65,71,63,64,69,69,63 (69 at 1,3,8,9th). Third row:67,65,66,69,63,68,67,71,70,66 (69 at 4th). So total 6 (first row) +4 (second row) +1 (third row) = 11? Wait no: first row 69:1. Second row:69 (1st),69 (3rd),69 (8th),69 (9th):4. Third row:69 (4th):1. Total 1+4+1=6? Wait no, let's list all 69s:

Data points:

1:68, 2:66, 3:72, 4:65, 5:67, 6:69, 7:70, 8:63, 9:63, 10:67,

11:69, 12:63, 13:69, 14:65, 15:64, 16:69, 17:69, 18:63, 19:67, 20:65,

21:66, 22:69, 23:63, 24:68, 25:67, 26:71, 27:70, 28:66, 29:71, 30:72? Wait no, original data: third row is 67,65,66,69,63,68,67,71,70,66 (10 elements). So total 10+10+10=30. So 69s:

First row: 6th (69) →1

Second row:1st (69),3rd (69),8th (69),9th (69) →4

Third row:4th (69) →1

Total:1+4+1=6? Wait no, 1 (row1) +4 (row2) +1 (row3) =6? Wait no, 6+4+1=11? Wait I must have miscounted. Let's count all 69s:

List all 69s:

From first row: 69 (1 number)

Second row: 69,69,69,69 (4 numbers)

Third row: 69 (1 number)

Total:1+4+1=6? Wait no, 1+4=5, +1=6? Wait no, first row: 69 (1), second row: 69 (1),69 (3),69 (8),69 (9) →4, third row:69 (4) →1. So 1+4+1=6? Wait but let's count the numbers:

First row elements: 68,66,72,65,67,69,70,63,63,67 → 10 numbers, 1 six-nine.

Second row:69,63,69,65,71,63,64,69,69,63 → 10 numbers, 4 six-nines (positions 1,3,8,9).

Third row:67,65,66,69,63,68,67,71,70,66 → 10 numbers, 1 six-nine (position 4).

Total six-nines:1+4+1=6? Wait no, 1+4=5, +1=6? Wait 1 (first) +4 (second) =5, +1 (third)=6. Yes.

Step8: Count frequency of 70

70 appears at first row 7th, third row 9th. So 2 times.

Step9: Count frequency of 71

71 appears at second row 5th, third row 8th. So 2 times.

Step10: Count frequency of 72

72 appears at first row 3rd. So 1 time.

Answer:

Height	Frequency
64	1
65	3
66	3
67	4
68	2
69	6	Wait no, earlier count was wrong. Wait recheck 69:

Wait second row:69,63,69,65,71,63,64,69,69,63 → that's 4 six-nines (indices 0,2,7,8 if 0-based). First row: index 5 (69). Third row: index 3 (69). So total 1 (first) +4 (second) +1 (third) =6? Wait no, 1+4=5, +1=6. But let's list all 69s:

Numbers: 69,69,69,69,69,69? Wait no, first row:1, second row:4, third row:1 → total 6.

Wait 70: first row 70 (1), third row 70 (1) → 2.

71: second row 71 (1), third row 71 (1) → 2.

72: first row 72 (1) →1.

So the frequency table:

63:6, 64:1, 65:3, 66:3, 67:4, 68:2, 69:6, 70:2, 71:2, 72:1.

Wait but let's verify total:6+1+3+3+4+2+6+2+2+1= 6+1=7, +3=10, +3=13, +4=17, +2=19, +6=25, +2=27, +2=29, +1=30. Correct, since there are 30 students.