Question

the stem-and-leaf plot below gives the test scores for ms. carter’s science classes. there were 16 students in fourth period and 21 in fifth period. use the plot to answer the questions.
score on ms. carter’s science test
fourth period fifth period
6 2 1 | 4 | 3
9 4 | 5 | 1 2 3 4
5 5 1 | 6 | 3
0 | 7 | 2 4 5
4 | 8 | 3 5 6
5 5 5 0 0 0 | 9 | 0 0 0 3 3 4 7 8 9
(a) which class had the greater median test score?
○ fourth period ○ fifth period ○ the medians were the same
(b) what were the ranges of test scores for the two classes?
fourth period
fifth period
(c) which class had more test scores in the 90s?
○ fourth period ○ fifth period ○ each had the same

Explanation:

Part (a)

Step1: Find median for Fourth period

Fourth period has 16 students (even number). Median is average of 8th and 9th terms.
List scores: 41, 42, 46, 54, 59, 61, 65, 65, 70, 84, 90, 90, 90, 95, 95, 95
8th term: 65, 9th term: 70. Median = $\frac{65 + 70}{2} = 67.5$

Step2: Find median for Fifth period

Fifth period has 21 students (odd number). Median is 11th term.
List scores: 43, 51, 52, 53, 54, 63, 72, 74, 75, 83, 85, 86, 90, 90, 90, 93, 93, 94, 97, 98, 99
11th term: 85

Step3: Compare medians

67.5 < 85, so Fifth period has greater median.

Step1: Range for Fourth period

Range = Max - Min. Max = 95, Min = 41. Range = 95 - 41 = 54

Step2: Range for Fifth period

Range = Max - Min. Max = 99, Min = 43. Range = 99 - 43 = 56

Step1: Count 90s in Fourth period

Scores in 90s: 90, 90, 90, 95, 95, 95 (6 scores)

Step2: Count 90s in Fifth period

Scores in 90s: 90, 90, 90, 93, 93, 94, 97, 98, 99 (9 scores)

Step3: Compare counts

6 < 9, so Fifth period has more.

Answer:

Fifth period

Part (b)