Question

the stem-and-leaf plot below gives the test scores for ms. carter’s science classes. there were 18 students in fourth period and 17 in fifth period. use the plot to answer the questions. score on ms. carter’s science test fourth period fifth period 5 5 4 8 8 6 6 4 1 0 6 0 4 6 8 9 9 9 6 0 7 1 3 4 5 6 6 8 6 6 8 1 1 5 9 6 5 9 5 8 (a) what were the ranges of test scores for the two classes? fourth period fifth period (b) which class had more test scores in the 50s? fourth period fifth period each had the same (c) which class had the greater median test score? fourth period fifth period the medians were the same

Explanation:

Step1: Find range for Fourth period

Range = Max - Min. For Fourth period, min score is 55 (stem 5, leaf 5), max score is 99 (stem 9, leaf 9? Wait, stem 9 leaves: 9,6,5? Wait, stem is tens place, leaf is ones. So Fourth period scores: 55, 60,61,64,66,66,68,68, 70,76,79,79,79? Wait no, stem 7: leaves 9,9,6,0? Wait the stem-and-leaf plot:

Fourth period:
Stem 5: leaf 5 → 55
Stem 6: leaves 0,1,4,6,6,8,8 → 60,61,64,66,66,68,68 (wait, count: 0,1,4,6,6,8,8 → 7 scores? Wait original says 18 students. Let's list all:

Stem 5: 55 (1)
Stem 6: 60,61,64,66,66,68,68 (7) → total 8
Stem 7: 70,76,79,79,79? Wait no, stem 7 leaves: 0,6,9,9,9? Wait the plot: "9 9 6 0" under stem 7? Wait maybe typo, should be 0,6,9,9,9? Wait no, the plot shows "9 9 6 0" → 0,6,9,9? Wait no, the order is left to right? Wait the stem is 7, so 70,76,79,79 (4 scores) → total 8+4=12
Stem 8: leaves 6,6,8 → 86,86,88 (3) → 15
Stem 9: leaves 5,6,9 → 95,96,99 (3) → 18. Yes, 1+7+4+3+3=18. So min is 55, max is 99. Range = 99 - 55 = 44? Wait no, 99-55=44? Wait 99-55=44? Wait 99-55=44. Wait no, 99-55=44? Wait 55 to 99: 99-55=44.

Wait Fifth period:
Stem 5: leaf 4 → 54
Stem 6: leaves 0,4,6,8,9 → 60,64,66,68,69 (5)
Stem 7: leaves 1,3,4,5,6,6 → 71,73,74,75,76,76 (6)
Stem 8: leaves 1,1,5 → 81,81,85 (3)
Stem 9: leaves 5,8 → 95,98 (2)
Total: 1 (54) +5 (60-69)+6 (70-79)+3 (80-89)+2 (90-99)=17, correct.

Min for Fifth period: 54, max: 98. Range = 98 - 54 = 44? Wait no, 98-54=44? Wait 54 to 98: 98-54=44? Wait no, 98-54=44? Wait 54+44=98. Yes. Wait but wait Fourth period max: 99, min 55: 99-55=44? Wait 99-55=44. Fifth period: 98-54=44? Wait no, 98-54=44? Wait 54 to 98: 98-54=44. Wait that can't be. Wait maybe I made a mistake.

Wait Fourth period stem 9: leaves 5,6,9 → 95,96,99. So max is 99. Min is 55 (stem 5, leaf 5). So range: 99 - 55 = 44.

Fifth period: stem 5: 54, stem 9: 98. So max 98, min 54. Range: 98 - 54 = 44? Wait 98-54=44. Wait that's same? But maybe I miscalculated.

Wait no, Fourth period: 99-55=44. Fifth period: 98-54=44. Wait but let's check again.

Wait Fourth period:

Stem 5: 55 (1)
Stem 6: 60,61,64,66,66,68,68 (7) → 8
Stem 7: 70,76,79,79,79? Wait no, stem 7 leaves: 0,6,9,9,9? Wait the plot says "9 9 6 0" → 0,6,9,9 (4 scores: 70,76,79,79) → 8+4=12
Stem 8: 86,86,88 (3) → 15
Stem 9: 95,96,99 (3) → 18. Correct. So min 55, max 99. Range 99-55=44.

Fifth period:

Stem 5: 54 (1)
Stem 6: 60,64,66,68,69 (5) → 6
Stem 7: 71,73,74,75,76,76 (6) → 12
Stem 8: 81,81,85 (3) → 15
Stem 9: 95,98 (2) → 17. Correct. Min 54, max 98. Range 98-54=44. Wait, so both ranges are 44? But maybe I made a mistake. Wait 99-55=44, 98-54=44. Yes.

Step2: Part (b): Scores in 50s. Fourth period: stem 5, leaf 5 → 55 (1 score). Fifth period: stem 5, leaf 4 → 54 (1 score)? Wait no, Fourth period: stem 5, leaf 5 → 55 (1). Fifth period: stem 5, leaf 4 → 54 (1). Wait but the options: Fourth period, Fifth period, same. Wait no, maybe I misread. Wait the plot: Fourth period stem 5: leaf 5 (1), Fifth period stem 5: leaf 4 (1). Wait but the question is "more test scores in the 50s". Wait 50s: scores from 50-59. Fourth period: 55 (1). Fifth period: 54 (1). Wait same? But the options include "Each had the same". Wait but maybe I made a mistake. Wait Fourth period: stem 5, leaf 5 → 55 (1). Fifth period: stem 5, leaf 4 → 54 (1). So same number. But wait the plot: Fourth period stem 5: 5 (1), Fifth period stem 5: 4 (1). So each has 1. So answer is "Each had the same".

Step3: Part (c): Median. Fourth period has 18 students (even number), median is average of 9th and 10th scores. Let's list Fourth period scores in order:

55,
60,61,64,66,66,68,68,
70,76,79,79,79,
86,86,88,
95,96,99

Wait no, wait stem 7: leaves 0,6,9,9,9? Wait no, earlier I thought 0,6,9,9 but maybe it's 0,6,9,9,9? Wait the plot says "9 9 6 0" → maybe 0,6,9,9 (four leaves). Wait no, 18 students:

1 (55) +7 (stem 6) +4 (stem 7) +3 (stem 8) +3 (stem 9) = 1+7=8, +4=12, +3=15, +3=18. So stem 7: 4 scores: 70,76,79,79.

So ordered list:

1:55

2:60

3:61

4:64

5:66

6:66

7:68

8:68

9:70

10:76

11:79

12:79

13:86

14:86

15:88

16:95

17:96

18:99

Wait no, 18th is 99. So 9th score: 70, 10th score:76. Median = (70 +76)/2 =73.

Fifth period: 17 students (odd), median is 9th score (since (17+1)/2=9th). Let's list Fifth period scores:

1:54

2:60

3:64

4:66

5:68

6:69

7:71

8:73

9:74

10:75

11:76

12:76

13:81

14:81

15:85

16:95

17:98

Wait ordered:

54,

60,64,66,68,69,

71,73,74,75,76,76,

81,81,85,

95,98

Wait 17 scores: positions 1-17. 9th score: 74.

Fourth period median: (70 +76)/2=73. Fifth period median:74. So Fifth period has greater median.

Answer:

(a) Fourth period: $\boxed{44}$, Fifth period: $\boxed{44}$
(b) $\boxed{\text{Each had the same}}$
(c) $\boxed{\text{Fifth period}}$