Question

a phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown.
o o a o o
b o b a o
ab b a b b
a o a b o
a o a o a
ab a a ab a
a o a a o
o ab o o o
o a o o o
o a o a o
construct a frequency distribution.
\begin{tabular}{|c|c|}
hline blood type & frequency \\
hline a & \\
hline ab & \\
hline b & \\
hline o & \\
hline end{tabular}
(type whole numbers.)

Explanation:

Step1: Count Blood Type A

Go through the list and count how many times 'A' appears. Let's list the rows:
Row 1: O, O, A, O, O → 1 A
Row 2: B, O, B, A, O → 1 A
Row 3: AB, B, A, B, B → 1 A
Row 4: A, O, A, A, O → 3 A
Row 5: A, O, A, B, A → 3 A
Row 6: AB, A, A, O, A → 3 A
Row 7: A, A, O, AB, A → 3 A
Row 8: O, AB, O, A, O → 1 A
Row 9: O, A, O, O, O → 1 A
Row 10: O, A, O, A, O → 2 A

Now sum these: 1+1+1+3+3+3+3+1+1+2 = 19. Wait, maybe a better way: let's count each 'A' in the entire list. Let's list all the blood types:

First column: O, B, AB, A, A, AB, A, O, O, O → A's: 3
Second column: O, O, B, O, O, A, A, AB, A, A → A's: 4
Third column: A, B, A, A, A, A, O, O, O, O → A's: 4
Fourth column: O, A, B, A, B, O, AB, A, A, A → A's: 5
Fifth column: O, O, B, O, A, A, O, O, O, O → A's: 2

Wait, maybe I made a mistake earlier. Let's do it properly. Let's list all 50 entries:

Row 1 (5 entries): O, O, A, O, O → A:1
Row 2 (5): B, O, B, A, O → A:1
Row 3 (5): AB, B, A, B, B → A:1
Row 4 (5): A, O, A, A, O → A:3
Row 5 (5): A, O, A, B, A → A:3
Row 6 (5): AB, A, A, O, A → A:3
Row 7 (5): A, A, O, AB, A → A:3
Row 8 (5): O, AB, O, A, O → A:1
Row 9 (5): O, A, O, O, O → A:1
Row 10 (5): O, A, O, A, O → A:2

Now sum: 1+1=2; 2+1=3; 3+3=6; 6+3=9; 9+3=12; 12+3=15; 15+1=16; 16+1=17; 17+2=19. Wait, but let's check another way. Let's count each blood type:

Blood Type A: Let's list all A's. Let's go through each entry:

1. O
2. O
3. A → 1
4. O
5. O
6. B
7. O
8. B
9. A → 2
10. O
11. AB
12. B
13. A → 3
14. B
15. B
16. A → 4
17. O
18. A → 5
19. A → 6
20. O
21. A → 7
22. O
23. A → 8
24. B
25. A → 9
26. AB
27. A → 10
28. A → 11
29. O
30. A → 12
31. A → 13
32. A → 14
33. O
34. AB
35. A → 15
36. O
37. AB
38. A → 16
39. O
40. A → 17
41. O
42. A → 18
43. O
44. O
45. O
46. O
47. A → 19
48. O
49. A → 20? Wait, maybe I miscounted. Wait, the total number of patients is 50. Let's check other blood types.

Blood Type AB: Let's count AB's. Entries: 11 (AB), 26 (AB), 34 (AB), 37 (AB), 8 (AB)? Wait, row 8: O, AB, O, A, O → AB at position 2. Row 3: AB at position 1. Row 6: AB at position 1. Row 7: AB at position 4. So AB's: row3 (1), row6 (1), row7 (1), row8 (1), row11? Wait, no, let's list all AB's:

Entry 11: AB

Entry 26: AB

Entry 34: AB

Entry 37: AB

Entry 8: AB (row8, column2)

Wait, row3: column1: AB

row6: column1: AB

row7: column4: AB

row8: column2: AB

row26: Wait, no, the rows are 10 rows of 5, so entries 1-5 (row1), 6-10 (row2), 11-15 (row3), 16-20 (row4), 21-25 (row5), 26-30 (row6), 31-35 (row7), 36-40 (row8), 41-45 (row9), 46-50 (row10).

So AB's:

Entry 11 (row3, col1): AB

Entry 26 (row6, col1): AB

Entry 34 (row7, col4): AB

Entry 37 (row8, col2): AB

Wait, that's 4? Wait, row5: entry25? No, row5 is entries21-25: A, O, A, B, A → no AB. Row6: entries26-30: AB, A, A, O, A → AB at 26. Row7: entries31-35: A, A, O, AB, A → AB at 34. Row8: entries36-40: O, AB, O, A, O → AB at 37. Row3: entries11-15: AB, B, A, B, B → AB at 11. Any others? Row9: entries41-45: O, A, O, O, O → no. Row10: entries46-50: O, A, O, A, O → no. So AB: 4?

Blood Type B: Let's count B's. Entries:

Row2: entry6 (B), entry8 (B)

Row3: entry12 (B), entry14 (B), entry15 (B)

Row5: entry24 (B)

Row4: entry19? No, row4: A, O, A, A, O → no B. Row5: A, O, A, B, A → B at 24.

So B's:

Entry6 (row2, col1): B

Entry8 (row2, col3): B

Entry12 (row3, col2): B

Entry14 (row3, col4): B

Entry15 (row3, col5): B

Entry24 (row5, col4): B

Wait, that's 6? Let's check:

Row2: B, O, B, A, O → B's at 6,8 → 2

Row3: AB, B, A, B, B → B's at 12,14,15 → 3

Row5: A, O, A, B, A → B at 24 → 1

Total B: 2+3+1=6.

Blood Type O: Total patients 50. So O = 50 - A - AB - B. Let's assume A is 19, AB is 4, B is 6. Then O = 50 -19 -4 -6 = 21. Let's check by counting O's.

O's: Let's list all O's.

Row1: O, O, A, O, O → 4

Row2: O, O, B, A, O → 3 (entries7,9,10)

Row3: AB, B, A, B, B → 0

Row4: A, O, A, A, O → 2 (entries17,20)

Row5: A, O, A, B, A → 1 (entry22)

Row6: AB, A, A, O, A → 1 (entry29)

Row7: A, A, O, AB, A → 1 (entry33)

Row8: O, AB, O, A, O → 3 (entries36,38,40)

Row9: O, A, O, O, O → 4 (entries41,43,44,45)

Row10: O, A, O, A, O → 3 (entries46,48,50)

Now sum these O's:

Row1:4

Row2:3 → 7

Row3:0 →7

Row4:2 →9

Row5:1 →10

Row6:1 →11

Row7:1 →12

Row8:3 →15

Row9:4 →19

Row10:3 →22. Wait, that's 22. Then A + AB + B + O = 19 +4 +6 +22=51. Oh, I must have miscounted A's. Let's re-count A's.

Let's list all A's with their positions:

Row1: entry3 →1

Row2: entry9 →2

Row3: entry13 →3

Row4: entries16,18,19 →3 (total 6)

Row5: entries21,23,25 →3 (total 9)

Row6: entries27,28,30 →3 (total 12)

Row7: entries31,32,35 →3 (total 15)

Row8: entry39 →16

Row9: entry42 →17

Row10: entries47,49 →2 (total 19). Wait, but O's were 22, AB 4, B 6: 19+4+6+22=51. There's an extra. So I must have miscounted O's.

Let's count O's again carefully:

Row1 (entries1-5): O(1), O(2), A(3), O(4), O(5) → 4 O's

Row2 (entries6-10): B(6), O(7), B(8), A(9), O(10) → O(7), O(10) → 2 O's (wait, earlier I said 3, that's mistake! Entry7: O, entry10: O → 2, not 3. So row2: 2 O's.

Row3 (entries11-15): AB(11), B(12), A(13), B(14), B(15) → 0 O's

Row4 (entries16-20): A(16), O(17), A(18), A(19), O(20) → O(17), O(20) → 2 O's

Row5 (entries21-25): A(21), O(22), A(23), B(24), A(25) → O(22) → 1 O

Row6 (entries26-30): AB(26), A(27), A(28), O(29), A(30) → O(29) → 1 O

Row7 (entries31-35): A(31), A(32), O(33), AB(34), A(35) → O(33) → 1 O

Row8 (entries36-40): O(36), AB(37), O(38), A(39), O(40) → O(36), O(38), O(40) → 3 O's

Row9 (entries41-45): O(41), A(42), O(43), O(44), O(45) → O(41), O(43), O(44), O(45) → 4 O's

Row10 (entries46-50): O(46), A(47), O(48), A(49), O(50) → O(46), O(48), O(50) → 3 O's

Now sum O's:

Row1:4

Row2:2 →6

Row3:0 →6

Row4:2 →8

Row5:1 →9

Row6:1 →10

Row7:1 →11

Row8:3 →14

Row9:4 →18

Row10:3 →21. There we go, 21 O's.

Now A's: Let's count again, correctly.

Row1: entry3 →1

Row2: entry9 →2

Row3: entry13 →3

Row4: entries16,18,19 →3 (total 6)

Row5: entries21,23,25 →3 (total 9)

Row6: entries27,28,30 →3 (total 12)

Row7: entries31,32,35 →3 (total 15)

Row8: entry39 →16

Row9: entry42 →17

Row10: entries47,49 →2 (total 19). Wait, but 19 + AB + B + 21 = 50 → AB + B = 10.

AB's: Let's count again.

Row3: entry11 →1

Row6: entry26 →2

Row7: entry34 →3

Row8: entry37 →4

Any others? Row9: no. Row10: no. So AB=4. Then B=10-4=6. Let's check B's:

Row2: entries6,8 →2

Row3: entries12,14,15 →3

Row5: entry24 →1

Total B: 2+3+1=6. Perfect, 19+4+6+21=50.

So:

Blood Type A: 19

Blood Type AB: 4

Blood Type B: 6

Blood Type O: 21

Step2: Fill the Frequency Table

Now we can fill the frequency table:

- A: 19
- AB: 4
- B: 6
- O: 21

Answer:

Blood Type	Frequency
AB	4
B	6
O	21