QUESTION IMAGE
Question
height (inches)
60 62 64 66 68 70 72 74 76
which of the following statements is supported by the boxplot?
a
the mean height is 67 inches.
b
the number of people with height at least 70 inches is greater than the number of people with height at most 62 inches.
c
the number of people with height at least 67 inches is less than the number of people with height at most 67 inches.
- Option A: Boxplots show median, quartiles, etc., not mean. So A is wrong.
- Option B: "At least 70" is the upper whisker and upper quartile region; "at most 62" is the lower whisker/quartile. The upper region (≥70) has less data than the lower (≤62) in a typical boxplot (since 62 is left, 70 is right, and middle 50% is between Q1 - Q3, so ≤62 is Q1 left, ≥70 is Q3 right; Q1 - 62 and 70 - Q3: usually Q1 - 62 has more? Wait, no—wait, the boxplot's whiskers: the lower quartile (Q1) and upper quartile (Q3). "At least 70" is data ≥70 (above Q3), "at most 62" is data ≤62 (below Q1). In a boxplot, the number of data points below Q1 and above Q3: if the distribution is symmetric, but here, 62 is left, 70 is right. Wait, maybe I messed up. Wait, the correct option is C? Wait no, let's re - evaluate. Wait, the question is which is supported. Wait, option C: "The number of people with height at least 67 inches is less than the number with height at most 67 inches." Let's think about the median. If 67 is around the median (since boxplot's line is median). The median splits data into two equal halves: at most median and at least median. Wait, but maybe 67 is the median? Wait, the boxplot's scale: 60,62,64,66,68,70,72,74,76. If the median is around 67? Wait, no, the boxplot's median line. But if we consider that "at most 67" includes the lower half (and maybe more if median is 67), and "at least 67" includes the upper half. But if the distribution is such that the lower half (at most 67) has more? Wait, no—wait, the correct approach: Boxplots represent quartiles. The median (Q2) divides the data into two equal parts: 50% at most median, 50% at least median. But if 67 is the median, then at most 67 and at least 67 would be equal. But maybe 67 is not the median. Wait, maybe the correct option is C? Wait, no, let's check the options again. Wait, the original problem: the boxplot's x - axis is height. Let's assume that the median is around 67. Wait, no, maybe the key is that in a boxplot, the number of data points at least a value and at most a value: if the value is the median, they are equal. But if the value is between Q1 and Q3, but here, let's think about the options:
Option A: Mean can't be determined from boxplot (boxplot shows median, quartiles, outliers). So A is incorrect.
Option B: "At least 70" (upper tail) and "at most 62" (lower tail). In a boxplot, the lower tail (≤62) and upper tail (≥70): usually, the lower tail has more data? No, wait, the length of the whiskers: if the lower whisker is from 60 to Q1 (say 62), and upper whisker from Q3 (say 70) to 76. The number of data points below Q1 (≤62) and above Q3 (≥70): in a boxplot, the number of points in each tail is less than 25% (since Q1 is 25th percentile, Q3 is 75th). So "at least 70" is above Q3 (25% of data), "at most 62" is below Q1 (25% of data). So they should be equal (if no outliers), so B is wrong.
Option C: "At least 67" and "at most 67". If 67 is the median (Q2), then at most 67 is 50% and at least 67 is 50%—but maybe 67 is not the median. Wait, maybe the boxplot's median is 67? Or maybe the distribution is skewed. Wait, maybe the correct answer is C? Wait, no, let's re - read. Wait, the problem is a multiple - choice, and the correct option is C? Wait, no, maybe I made a mistake. Wait, the key is: Boxplots show the median (which splits data into two equal parts: 50% ≤ median, 50% ≥ median). If 67 is the median, then at most 67 and at least 67 are equal. But if 67 is between Q1 and Q3, but the number of people at least 67: if 67 is above the median, then at most 67 woul…
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
C. The number of people with height at least 67 inches is less than the number of people with height at most 67 inches.