Question

the stem-and-leaf plot below gives the test scores for mr. uzuns english classes. there were 19 students in fourth period and 12 in fifth period. use the plot to answer the questions.
score on mr. uzuns english test
fourth period fifth period
6 | 5 2 3 3
7 6 3 | 6 3 3 6 8
8 5 4 3 3 | 7 0 1 2 7
2 2 2 1 0 | 8 6
8 8 3 0 0 | 9
(a) which class had the greater median test score?
fourth period fifth period the medians were the same
(b) which class had more test scores in the 50s?
fourth period fifth period each had the same
(c) what were the ranges of test scores for the two classes?
fourth period
fifth period

Explanation:

Step1: Find Fourth period median

For 19 data points, median is the 10th value. Ordered scores: 56, 63, 66, 67, 73, 73, 74, 75, 78, 80, 81, 82, 82, 82, 90, 90, 93, 98, 98. 10th value = 80.

Step2: Find Fifth period median

For 12 data points, median is average of 6th and 7th values. Ordered scores: 52, 53, 63, 63, 66, 68, 70, 71, 72, 77, 86. Wait, corrected: 12 values: 52,53,63,63,66,68,70,71,72,77,86? No, full list: 52,53,63,63,66,68,70,71,72,77,86? No, 12 values: 52,53,63,63,66,68,70,71,72,77,86 is 11. Oh, 52,53,63,63,66,68,70,71,72,77,86 – no, stem 5:2,3; stem6:3,3,6,8; stem7:0,1,2,7; stem8:6. That's 2+4+4+1=11? No, problem says 12. Wait, no, stem 9: fifth period has none. Wait, problem says 12 students. Oh, typo? No, recheck: 52,53,63,63,66,68,70,71,72,77,86 – missing one. Wait no, stem 7: 0,1,2,7 is 4, stem6:4, stem5:2, stem8:1. 2+4+4+1=11. But problem says 12. Wait, no, maybe I misread. Fifth period stem 8:6, stem7:0,1,2,7; stem6:3,3,6,8; stem5:2,3. That's 2+4+4+1=11. But problem says 12. Wait, no, maybe the plot has stem 9? No. Wait, maybe I made a mistake in median calculation. For n=12, median is average of 6th and 7th. 6th value is 68, 7th is70. Median = $\frac{68+70}{2}=69$. Compare to 80, so fourth period median is higher.

Step3: Count 50s scores

Fourth period 50s: 56 (1 score). Fifth period 50s:52,53 (2 scores). So fifth period has more.

Step4: Calculate Fourth period range

Range = Max - Min. Max=98, Min=56. Range = $98-56=42$.

Step5: Calculate Fifth period range

Max=86, Min=52. Range = $86-52=34$.

Answer:

(a) Fourth period
(b) Fifth period
(c) Fourth period: 42
Fifth period: 34