Question

which of the following best describes the shape of the distribution pictured below?
image of a histogram
stem and leaf
stem | leaf | count
9 | 0000222444555789 | 17
8 | 011244666788899 | 14
7 | 0033345788888999 | 15
6 | 01124555557779 | 12
5 | 02222333457778999 | 16
4 | 001134455566666799 | 17
3 | 012234456667789 | 14
2 | 11233355678889 | 13
1 | 001234456777888999 | 16
0 | 00133477899 | 11
0|0 represents 0.00

options:

• skewed left and unimodal
• skewed right and bimodal
• symmetric and unimodal
• uniform
• skewed left and bimodal
• skewed right and unimodal

Explanation:

1. Symmetry Check: A symmetric distribution has data balanced around the center. The stem - leaf plot (and histogram) should have similar counts on either side of the middle. Looking at the counts for each stem (e.g., stem 0 has 11, stem 1 has 16; stem 9 has 17, stem 8 has 14), the counts are relatively balanced around the middle stems (4,5,6,7).
2. Modality Check: A unimodal distribution has one main peak. The histogram (and stem - leaf plot) doesn't show two distinct peaks (so not bimodal) and doesn't have roughly equal bar heights (so not uniform). It has one general peak area, so unimodal. Skewness: Since it's balanced, it's not skewed left or right. So the distribution is symmetric and unimodal.

Answer:

Symmetric and unimodal