Question

here is a data set summarized as a stem-and-leaf plot:
6# | 12224569
7# | 00012235678888889
8# | 04468
9# | 046

how many data values are in this data set?
n = 32 ✔️

what is the minimum value in the last class?
ans = 90 ✔️

what is the frequency of the modal class? (hint, what is the mode?)
frequency = 16 ✔️

how many of the original values are greater than 80?
ans = 8 ❌
enter an integer or decimal number more..

Explanation:

Step1: Identify classes >80

Classes with stem >8: 8# and 9#.

Step2: Count 8# values

Stem 8#: leaves 0,4,4,6,8 → 5 values.

Step3: Count 9# values

Stem 9#: leaves 0,4,6 → 3 values.

Step4: Sum counts

Total = 5 + 3 = 8? Wait, no—wait, 8# is 80 - 89, 9# is 90 - 99. Wait, original data: 8# has 5 (0,4,4,6,8 → 80,84,84,86,88), 9# has 3 (0,4,6 → 90,94,96). Wait, but maybe I miscounted? Wait 8#: 0,4,4,6,8 → 5. 9#: 0,4,6 → 3. 5+3=8? But the system marked it wrong. Wait, no—wait, the stem is 8#: so the numbers are 80,84,84,86,88 (5 numbers). 9#: 90,94,96 (3 numbers). Wait, but maybe the stem is 8# meaning 80s, 9# meaning 90s. Wait, but let's recheck:

Stem 6#: 1,2,2,2,4,5,6,9 → 8 values (61,62,62,62,64,65,66,69)
Stem 7#: 0,0,0,1,2,2,3,5,6,7,8,8,8,8,8,9 → 16 values (70,70,70,71,72,72,73,75,76,77,78,78,78,78,78,79)
Stem 8#: 0,4,4,6,8 → 5 values (80,84,84,86,88)
Stem 9#: 0,4,6 → 3 values (90,94,96)

Wait, total data values: 8+16+5+3=32, which matches. Now, values greater than 80: so 81 and above? Wait, no—80 is 80, so values greater than 80 would be 81+, but in stem 8#, the leaves are 0,4,4,6,8 → 80,84,84,86,88. So 80 is equal to 80, not greater. So values greater than 80: 84,84,86,88 (from 8#) and 90,94,96 (from 9#). Wait, that's 4 + 3 = 7? Wait, no: 80 is not greater than 80, so 8#: leaves 4,4,6,8 (4 values: 84,84,86,88) and 9#: 3 values (90,94,96). So 4+3=7? Wait, maybe the stem is 8# meaning 80-89, so numbers are 80,84,84,86,88. So "greater than 80" would exclude 80. So 84,84,86,88 (4) + 90,94,96 (3) = 7. Wait, but the initial answer was 8, which was wrong. Wait, maybe the stem is 8#: the numbers are 80,84,84,86,88 (5 numbers). If "greater than 80" includes 80? No, "greater than" means >80, so 80 is not included. Wait, maybe the problem is "greater than or equal to 80"? But the question says "greater than 80". Wait, let's re-express:

Stem 8#: 80,84,84,86,88 → values: 80,84,84,86,88. So values >80: 84,84,86,88 (4)
Stem 9#: 90,94,96 → all >80 (3)
Total: 4 + 3 = 7. Wait, but maybe I made a mistake. Wait, let's count again:

Stem 8#: leaves 0,4,4,6,8 → 5 numbers: 80,84,84,86,88. So numbers greater than 80: 84,84,86,88 (4 numbers)
Stem 9#: leaves 0,4,6 → 3 numbers: 90,94,96 (all >80)
Total: 4 + 3 = 7.

Wait, but maybe the stem is 8#: the first digit is 8, so the numbers are 80-89, so 80 is 80, 84 is 84, etc. So "greater than 80" would be 81-89 and 90-99. But in stem 8#, the leaves are 0,4,4,6,8 → 80,84,84,86,88. So 80 is 80, not greater. So 84,84,86,88 (4) and 90,94,96 (3) → 7.

Alternatively, maybe the problem is "greater than or equal to 80", but the question says "greater than". Wait, maybe I miscounted the stem 8#. Let's check the stem 8#: "8# | 04468" → the leaves are 0,4,4,6,8 → that's 5 leaves. So 5 numbers: 80,84,84,86,88. Stem 9#: "9# | 046" → 3 leaves: 90,94,96. So numbers greater than 80: 84,84,86,88 (4) + 90,94,96 (3) = 7. So the correct answer should be 7.

Wait, but let's re-express the problem: "How many of the original values are greater than 80?" So values >80. So 80 is not included. So:

• 8#: values are 80,84,84,86,88. So >80: 84,84,86,88 → 4
• 9#: 90,94,96 → all >80 → 3

Total: 4 + 3 = 7.

So the correct answer is 7.

Answer:

7