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The number of bagels sold daily for two bakeries is shown in the table:


Bakery A Bakery B
45 48
52 42
51 11
48 45
57 57
30 10
55 43
46 46


Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
Mean for both bakeries because the data is symmetric
Mean, because the distribution is symmetric for both bakeries
Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric

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SaniShahbaz

Answer:

Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be observed from the stem and leaf frequency plot.

Step-by-step explanation:

CALCULATIONS FOR BAKERY A

Considering the data for Bakery A

45 52 51 48 57 30 55 46

Calculating Mean for Bakery A

[tex]Mean=\frac{Sum\:of\:terms}{Number\:of\:terms}[/tex]

Sum of terms = 45 + 52 + 51 + 48 + 57 + 30 + 55 + 46 = 384

Number of terms = 8

As

[tex]Mean=\frac{Sum\:of\:terms}{Number\:of\:terms}[/tex]

[tex]Mean=\frac{302}{8}[/tex]

[tex]Mean=48[/tex]

Calculating Median for Bakery A

As the median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

As the data for Bakery A is

45 52 51 48 57 30 55 46

Ordering the data from least to greatest, we get:

30   45   46   48   51  52   55   57  

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

[tex]Median=\frac{\left(48+51\right)}{2}=\frac{99}{2}=49.5[/tex]

Getting a Plot and Leaf Plot for Bakery A

  • Plot and leaf plot is generally a unique table-like diagram which displays the frequency distribution of a data set.
  • Plot and leaf plot is a visual aid that supports us in recognizing frequency classes and the center of the distribution where most of the data gets clustered around.

Data for Bakery A in ascending order

30   45   46   48   51  52   55   57  

STEM                    LEAF

3                               0

4                               5   6   8

5                               1    2   5   7

CALCULATIONS FOR BAKERY B

Considering the data for Bakery B

48 42 11 45 57 10 43 46

Calculating Median for Bakery B

[tex]Mean=\frac{Sum\:of\:terms}{Number\:of\:terms}[/tex]

Sum of terms = 48 + 42 + 11 + 45 + 57 + 10 + 43 + 46 = 302

Number of terms = 8

[tex]Mean=\frac{302}{8}=37.75[/tex]

Calculating Median for Bakery B

[tex]Median=\frac{\left(43+45\right)}{2}=44[/tex]

Getting a Plot and Leaf Plot for Bakery B

Data for Bakery B in ascending order

10   11   42   43   45   46   48   57  

STEM                    LEAF

1                               0   1

2                              

3                              

4                              2   3   5   6   8

5                              7

So, from the above observation, we can conclude that Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be observed from the stem and leaf frequency plot.

Keywords: symmetric distribution, mean, media

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Answer:

Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be observed from the stem and leaf frequency plot.

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