Question

Adriana counted all the beads in each necklace at the jewelry store where she works.
Beads per necklace
Stem Leaf
1 2 7
2 6 7
3 0 1 2 4 6 8 9 9 9
4 0 3 4 9
5
6 1 4 6
7 4 7 9
8
9 0

Answer 1

Here’s a clean reading of the stem-and-leaf and a set of summary statistics.

Data (stem = tens, leaf = units), sorted:
12, 17, 26, 27, 30, 31, 32, 34, 36, 38, 39, 39, 39, 40, 43, 44, 49, 61, 64, 66, 74, 77, 79, 90

Frequencies by decade:
- 10s: 2
- 20s: 2
- 30s: 9
- 40s: 4
- 50s: 0
- 60s: 3
- 70s: 3
- 80s: 0
- 90s: 1

Summary statistics:
- Count (n): 24
- Minimum: 12
- Maximum: 90
- Range: 90 − 12 = 78
- Mean: 1087 / 24 ≈ 45.29
- Median: (12th + 13th)/2 = (39 + 39)/2 = 39
- Mode: 39 (appears 3 times)
- First quartile (Q1): median of lower half = 31.5
- Third quartile (Q3): median of upper half = 62.5
- Interquartile range (IQR): Q3 − Q1 = 31.0
- Sample standard deviation ≈ 20.5 (population SD ≈ 20.06)

Outliers (1.5·IQR rule):
- 1.5·IQR = 46.5, upper fence = Q3 + 46.5 = 109, lower fence = Q1 − 46.5 = −15.
- No outliers by this rule (all values between −15 and 109).

Shape/comment:
- The distribution is right-skewed (mean > median and a tail of larger values like 61, 64, 66, 74, 77, 79, 90). The 30s contain the largest concentration of necklaces.