Question

match the histogram with the word that best describes it. a. left skewed b. bell - shaped c. bimodal d. right skewed e. uniform

Explanation:

First Histogram (Top One)

Step1: Analyze Skewness Direction

A left - skewed (negatively skewed) distribution has a longer tail on the left side. In this histogram, the left - most bar (the first bar) is shorter, and the bars increase in height towards the left - most part of the peak and then decrease towards the right. Wait, no, actually, when we look at the histogram, the tail is on the left (the lower values have a shorter bar and the higher frequency is on the right - side of the left tail). Wait, let's correct: A right - skewed (positively skewed) distribution has a longer tail on the right. Wait, no, the first histogram: the bars start with a short bar on the left, then a tall bar, then bars decreasing in height as we move to the right. Wait, no, the left - most bar is short, then the next bar is tall, then the bars get shorter as we move to the right. Wait, actually, the tail is on the right? No, wait, skewness is determined by the tail. If the tail is on the right, it's right - skewed; if on the left, left - skewed. Wait, in this histogram, the left side (lower values) has a short bar, and the bars increase to a peak and then decrease towards the right. Wait, no, the first bar (left - most) is height 1, then 4, then 3, then 2, then 1. So the peak is on the left - middle, and the tail is on the right (the last bar is height 1, same as the first, but the bars after the peak (the 4 - height bar) decrease. Wait, actually, this is a right - skewed? No, wait, left - skewed: the tail is on the left, meaning the mean is less than the median. Wait, maybe I made a mistake. Wait, let's recall: In a left - skewed distribution, the left tail is longer (more spread out on the left). In the first histogram, the left - most bar is short, and the bars increase in height towards the center (the 4 - height bar) and then decrease towards the right. Wait, no, the first bar (left) is height 1, then 4, then 3, then 2, then 1. So the distribution has a peak, and the left tail (the bar at the left end) is short, and the right tail (the bar at the right end) is also short? Wait, no, maybe it's right - skewed? Wait, no, let's look at the options. The options are left - skewed, bell - shaped, bimodal, right - skewed, uniform.

Wait, the first histogram: the frequencies are 1, 4, 3, 2, 1. So it has a single peak, and the left side (the first bar) is shorter than the peak, and the right side has bars decreasing. Wait, actually, this is a right - skewed? No, wait, left - skewed: the tail is on the left. Wait, maybe I got it reversed. Let's think of the direction of the tail. If the tail is on the right (the higher - value end has a longer tail, i.e., the bars get shorter as we move to higher values), then it's right - skewed. In this histogram, as we move from left to right (increasing values), the bars go 1 (low value), 4 (higher), 3 (lower than 4), 2 (lower than 3), 1 (lower than 2). So the tail is on the right (the higher - value end has the bars getting shorter, forming a tail). So this is right - skewed? Wait, no, wait, left - skewed is when the tail is on the left (lower - value end has the tail). Wait, maybe I made a mistake. Let's check the second histogram.

Second Histogram (Bottom One)

Step1: Analyze the Shape

A uniform distribution has bars of approximately equal height, meaning that each class interval has roughly the same frequency. In the second histogram, all the bars have a height of approximately 3 (or very close), so the frequencies are uniform across the intervals.

For the First Histogram:

Wait, let's re - analyze. The first histogram: frequencies are 1, 4, 3, 2, 1. So it has a peak, and the left side (the first bar) is short, and the right side has bars decreasing. Wait, actually, this is a right - skewed? No, wait, left - skewed: the tail is on the left. Wait, maybe the first histogram is right - skewed? Wait, no, let's recall the definition: Right - skewed (positively skewed): the tail is on the right (higher values), mean > median. Left - skewed (negatively skewed): tail is on the left (lower values), mean < median.

In the first histogram, the left - most bar (lowest value) has frequency 1, then the next bar (higher value) has frequency 4, then 3, 2, 1. So the lower values (left) have a short bar, and the higher values (right) have bars decreasing. So the tail is on the right. So it's right - skewed (option d).

The second histogram has bars of equal height, so it's uniform (option e).

First Histogram Answer:

d. Right skewed

Second Histogram Answer:

e. Uniform

Answer:

Step1: Analyze the Shape

A uniform distribution has bars of approximately equal height, meaning that each class interval has roughly the same frequency. In the second histogram, all the bars have a height of approximately 3 (or very close), so the frequencies are uniform across the intervals.

For the First Histogram:

Wait, let's re - analyze. The first histogram: frequencies are 1, 4, 3, 2, 1. So it has a peak, and the left side (the first bar) is short, and the right side has bars decreasing. Wait, actually, this is a right - skewed? No, wait, left - skewed: the tail is on the left. Wait, maybe the first histogram is right - skewed? Wait, no, let's recall the definition: Right - skewed (positively skewed): the tail is on the right (higher values), mean > median. Left - skewed (negatively skewed): tail is on the left (lower values), mean < median.

In the first histogram, the left - most bar (lowest value) has frequency 1, then the next bar (higher value) has frequency 4, then 3, 2, 1. So the lower values (left) have a short bar, and the higher values (right) have bars decreasing. So the tail is on the right. So it's right - skewed (option d).

The second histogram has bars of equal height, so it's uniform (option e).

First Histogram Answer:

d. Right skewed

Second Histogram Answer:

e. Uniform