Answer / Explanation:
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The number of bagels sold daily for two bakeries is shown in the table:
Bakery A 45 52 51 48 61 34 55 46
Bakery B 48 42 25 45 57 10 43 46
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A) Mean for both bakeries because the data is symmetric
B) Median because the distribution is not symmetric for both bakeries
C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric
D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
Now going back to answering the question:
We need to understand that Plot and leaf plot is a unique table-like diagram that illustrates the frequency distribution of a data set. Plot and leaf plot is a visual aid that helps recognize frequency classes and the center of the distribution where most of the data cluster around. It also offers a fair idea of whether the data are symmetrical or skewed.
Bakery A:
Mean : 45
+
52
+
51
+
48
+
61
+
34
+
55
+
46 / 8 = 49
Median ( 34
, 45, 46, 48, 51, 52, 55, 61) = 48 + 51/2 = 49.5
STEM LEAF
3 4
4 5 6 8
5 1 2 5
6 1
Bakery B:
Mean = 48 + 42 + 25 + 45 + 57 + 10 + 43 + 46 / 8 = 39.5
Median ( 10, 25, 42, 43, 45, 46, 48, 57 )= 43 + 45 / 2 = 41
STEM LEAF
1 0
2 5
4 2 3 5 6 8
5 7
Answer: D
Center of distribution is mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be inferred from the stem and leaf frequency distribution plot.
