Question

interpreting box plots

name:
date:
period:

1. ms. phillips, a math teacher, is recording test scores for her 72 students in her grade book. her results are shown in the box plot below.

a. what percentage of test scores are below an 85? ______
b. what percentage of test scores are between 65 and 100? ______
c. each quartile contains how many students? ______
d. how many students scored above a 65? ______
e. what is the range of the data? ______

Explanation:

Part a: Percentage below 85

Step1: Recall box plot quartiles

A box plot has 4 quartiles (Q1, Q2, Q3), each representing 25% of the data. Below Q3 (85 here), it's 75%? Wait, no: total data is 72 students. Wait, box plot: the median (Q2) splits into 50%, Q1 splits lower half, Q3 splits upper half. Wait, percentage below Q3: Q3 is the 75th percentile? Wait, no, quartiles: Q1 is 25th, Q2 50th, Q3 75th. So below Q3 (85) is 75%? Wait, but let's check. Wait, the total number of students is 72. Wait, maybe I misread. Wait, the problem says 72 students. Let's think again. Quartiles: each quartile is 25% of the data. So Q1: 25%, Q2: 50%, Q3: 75%. So below Q3 (85) is 75%? Wait, but let's calculate. 75% of 72: 0.75*72=54. But maybe the box plot: the median is at some point, Q1 and Q3. Wait, maybe the original problem: the box plot's Q3 is 85? Wait, the box plot shows the whiskers from ~45 to 100, box from ~65 to 90? Wait, maybe the Q3 is 85? Wait, the question is "what percentage of test scores are below an 85?". Since Q3 is the 75th percentile, so 75% of data is below Q3. So 75%? Wait, but let's confirm. In a box plot, the three quartiles (Q1, Q2, Q3) divide the data into four equal parts (25% each). So below Q3 (the third quartile) is 75% of the data. So percentage below 85 (if 85 is Q3) is 75%? Wait, maybe the answer is 75%? Wait, no, maybe I made a mistake. Wait, the total number of students is 72. Let's see: quartiles: each quartile has 72/4=18 students. So Q1: 25% (18), Q2: 50% (36), Q3: 75% (54). So below Q3 (85) is 54 students, which is 54/72=0.75=75%. So percentage is 75%.

Step2: Calculate percentage

Total students = 72. Quartile size = 72/4 = 18. Below Q3 (85) is 3 quartiles: 318=54. Percentage = (54/72)100 = 75%.

Step1: Identify the range

65 is Q1? Wait, the box plot: the lower whisker starts around 45, box starts at 65 (Q1), box ends at 90 (Q3), upper whisker to 100. Wait, between 65 (Q1) and 100: that's from Q1 to maximum. Q1 is 25th percentile, maximum is 100 (100th percentile). So the percentage is 100% - 25% = 75%? Wait, no: from Q1 (25th) to max (100th) is 75%? Wait, no, Q1 is 25th, so above Q1 is 75%? Wait, between 65 (Q1) and 100: that's the data from Q1 to the maximum. So percentage is 75%? Wait, let's calculate. Number of students between 65 and 100: total students - students below 65. Students below 65: Q1 is 25th percentile, so 25% of 72 = 18. So students between 65 and 100: 72 - 18 = 54. Percentage: (54/72)*100 = 75%. Wait, but maybe 65 is the minimum? No, the lower whisker is below 65. Wait, the box starts at 65, so 65 is Q1. So below Q1: 25% (18 students), so between Q1 (65) and max (100) is 75% (54 students). So percentage is 75%.

Step2: Calculate percentage

Students below 65: 25% of 72 = 18. Students between 65 and 100: 72 - 18 = 54. Percentage: (54/72)*100 = 75%.

Step1: Total students and quartiles

Total students = 72. A quartile divides data into 4 equal parts. So each quartile has 72 / 4 = 18 students.

Step2: Calculate

72 ÷ 4 = 18.

Answer:

75%

Part b: Percentage between 65 and 100