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question 1
determine the distribution of the data pictured below
box plot with data axis labeled 1, 2, 3, 4, 5
options: uniform, bell - shaped, skewed - right, skewed - left
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Question

score: 0/10  answered: 0/10
question 1
determine the distribution of the data pictured below
box plot with data axis labeled 1, 2, 3, 4, 5
options: uniform, bell - shaped, skewed - right, skewed - left
submit question

Accepted Answer

# Brief Explanations:
To determine the data distribution from the box - plot:
1. Recall the characteristics of different distributions:
   - A uniform distribution has data evenly spread, which is not the case here as the box - plot shows different lengths of whiskers and box parts.
   - A bell - shaped (normal) distribution has the box centered and whiskers of approximately equal length, which is not seen here.
   - For a skewed - right distribution, the left whisker is shorter than the right whisker, and the left part of the box (towards the lower values) is shorter. In the given box - plot, the left whisker (from 1 to the start of the box) is longer than the right whisker (from the end of the box to 5), and the left part of the box (near the lower values) is stretched out. Wait, no—wait, actually, in a skewed - left distribution, the left tail (whisker) is longer, and the box is shifted towards the right. Wait, let's re - examine:
   - The box - plot has the left whisker (from 1 to around 2.5) longer than the right whisker (from around 3.5 to 5). The median is around 3. The left side (lower values) has a longer tail. So the data is skewed - left? Wait, no, wait: Skewed - left means the tail is on the left (lower values), and the bulk of the data is on the right. Skewed - right means the tail is on the right (higher values), bulk on the left.
   - Wait, in the box - plot, the left whisker (from minimum to Q1) is longer than the right whisker (from Q3 to maximum). The box is between Q1 and Q3. If the left whisker is longer, that means the lower values are more spread out, so the distribution is skewed - left? Wait, no, I think I mixed up. Let's use the rule: In a box - plot, if the left whisker is longer than the right whisker, the distribution is skewed - left (negative skew), because the tail is on the left. If the right whisker is longer, it's skewed - right (positive skew).
   - Wait, the minimum is 1, Q1 is around 2.5, median around 3, Q3 around 3.5, maximum 5. So the left whisker length (Q1 - min = 2.5 - 1 = 1.5) is longer than the right whisker length (max - Q3 = 5 - 3.5 = 1.5? Wait, no, maybe my estimation is wrong. Wait, looking at the plot, the left whisker (from 1 to the box) is longer than the right whisker (from the box to 5). Wait, maybe the correct way: In a skewed - left distribution, the mean is less than the median, and the left tail is longer. In a skewed - right distribution, the mean is greater than the median, and the right tail is longer.
   - Wait, the box - plot here: the left whisker (lower end) is longer, so the data has a longer tail on the left, which means it's skewed - left? Wait, no, I think I made a mistake. Wait, let's check the options again. The options are Uniform, Bell - shaped, Skewed - right, Skewed - left.
   - Uniform: data is evenly distributed, so the box - plot would have whiskers of equal length and the box would be in the middle, but here the whiskers are not equal. Bell - shaped: symmetric, whiskers equal, box centered. Skewed - right: right whisker longer, box shifted left. Skewed - left: left whisker longer, box shifted right.
   - In the given plot, the left whisker (from 1 to the box) is longer than the right whisker (from the box to 5). So the distribution is skewed - left? Wait, no, wait the x - axis is from 1 to 5. The left whisker is from 1 to, say, 2.5, and the right whisker is from 3.5 to 5. The box is between 2.5 and 3.5? Wait, no, the box is split at 3. So Q1 is around 2.5, median 3, Q3 around 3.5. Then min is 1, max is 5. So left whisker length: 2.5 - 1 = 1.5, right whisker length: 5 - 3.5 = 1.5. Wait, maybe my initial perception was wrong. Wait, maybe the left tail (whisker) is longer. Wait, maybe the correct answer is Skewed - left? Wait, no, let's think again.
   - Wait, another way: In a skewed - left distribution, the lower values (left side) are more spread out, so the left whisker is longer. In the plot, the left whisker (from 1 to the box) is longer than the right whisker (from the box to 5). So the data is skewed - left. Wait, but maybe I got it reversed. Wait, no, let's check the definition: Skewness is a measure of the asymmetry of the probability distribution of a real - valued random variable about its mean. The skewness value can be positive, negative, or undefined. A positive skewness (skewed - right) means the tail on the right side of the distribution is longer or fatter. A negative skewness (skewed - left) means the tail on the left side is longer or fatter.
   - In the box - plot, the left whisker (lower values) is longer, so the tail is on the left, so it's skewed - left. Wait, but let's check the options. The options are Skewed - left, Skewed - right, etc. So the correct answer should be Skewed - left? Wait, no, maybe I made a mistake. Wait, the left whisker is from 1 to the box, and the right whisker is from the box to 5. The box is near the middle but the left whisker is longer. So the distribution is skewed - left.
# Answer:
D. Skewed - left

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