QUESTION IMAGE
Question
which of the following best describes the shape of the distribution pictured below? histogram (x-axis: 40,45,50,55,60; bars increasing to 50 then decreasing)
stem and leaf
stem | leaf | count
58 | 1 | 1
57 | 37 | 2
56 | 13 | 2
55 | 2369 | 4
54 | 012367 | 6
53 | 0234799 | 7
52 | 011112333689 | 11
51 | 00233335556777888 | 15
50 | 1222344455555666799 | 16
49 | 12223334444688 | 12
48 | 002689 | 6
47 | 11459 | 5
46 | 378 | 3
45 | 2367 | 4
44 | 23 | 2
43 | 0 | 1
42 | 059 | 3
42|0 represents 42.0
options:
○ uniform
○ skewed left and unimodal
○ skewed right and unimodal
○ skewed left and bimodal
Brief Explanations
- Unimodal Check: The histogram (and stem - leaf) has one main peak (around 50 - 51), so it's unimodal.
- Skewness Check: The tail on the right (higher values, like 57, 58) is longer than the left. Wait, no—wait, in skewness, left - skewed has a long left tail, right - skewed has a long right tail? Wait, no: Wait, the data: lower stems (42, 43, 44) have fewer counts, and as we go to higher stems (50, 51, 52), counts increase, then decrease. Wait, no, the tail on the right (higher values, like 57, 58) has fewer data points, and the left (lower values, 42 - 45) also has fewer, but the peak is in the middle. Wait, no, looking at the stem - leaf: the counts start low (42: 3, 43:1, 44:2, 45:4...), increase to a peak at 50 (16), then decrease (51:15, 52:11, 53:7, 54:6, 55:4, 56:2, 57:2, 58:1). So the tail on the right (higher stems, 55 - 58) is longer (extends more) than the left? Wait, no—left - skewed means the tail is on the left (lower values), right - skewed on the right (higher values). Wait, the lower values (42 - 45) have low counts, and the higher values (55 - 58) also have low counts, but the peak is in the middle. Wait, no, the left tail (lower values) is shorter, and the right tail (higher values) is longer? Wait, no, let's think about the direction of skewness. A right - skewed distribution has a longer tail on the right (higher values), meaning most data is on the left, with a long tail to the right. A left - skewed has a long tail on the left (lower values), most data on the right. Looking at the stem - leaf, the counts are low at the lower stems (42 - 45) and low at the higher stems (55 - 58), but the peak is at 50. Wait, no, the data from 42 to 45 is the left side, and 55 to 58 is the right side. The left side (42 - 45) has counts 3,1,2,4 (total 10), and the right side (55 - 58) has counts 4,2,2,1 (total 9). But the peak is at 50, and as we move to the right from 50 (51,52,53,54,55,56,57,58), the counts decrease: 15,11,7,6,4,2,2,1. As we move to the left from 50 (49,48,47,46,45,44,43,42), the counts decrease: 12,6,5,3,4,2,1,3. Wait, maybe I got it wrong. Wait, the histogram: the bars on the left (40 - 45) are short, and on the right (55 - 60) are also short, but the peak is in the middle. Wait, no, the option is "Skewed right and unimodal" or "Skewed left"? Wait, no—wait, when the tail is on the right (higher values), it's right - skewed. Wait, the data has a peak, and the tail on the right (higher numbers) is longer (extends more) than the left. Wait, the left side (lower numbers) has bars that are short, but the right side (higher numbers) also has short bars, but the peak is in the middle. Wait, no, the key is: in a right - skewed distribution, the mean is greater than the median, and the tail is on the right. In left - skewed, mean less than median, tail on left. Looking at the stem - leaf, the peak is at 50, and the data to the right of the peak (51 - 58) has a long tail (counts decrease gradually), while the data to the left (42 - 49) also decreases but maybe the right tail is longer. Wait, the option "Skewed right and unimodal"—unimodal because one peak, skewed right because the tail is on the right (higher values). Wait, no, wait the left tail (lower values) is shorter, right tail (higher values) is longer? Wait, no, the lower values (42 - 45) have low counts, and the higher values (55 - 58) also have low counts, but the peak is at 50. Wait, maybe the correct answer is "Skewed right and unimodal". Wait, no, let's re - examine: the stem - leaf shows that as we go from lower stems (42) to the peak stem (50)…
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
Skewed right and unimodal