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sixteen students each measured the weight of 25 pennies, in grams. the list shows their measurements. 60, 62, 65, 59, 63, 63, 63, 62, 64, 62, 60, 61, 66, 64, 61, 65 in each graph below, the mean is indicated by a solid vertical line segment while the standard deviations from the mean are indicated by dotted vertical line segments. which graph represents the distribution of weights?

sixteen students each measured the weight of 25 pennies in grams the list shows their measurements 60 62 65 59 63 63 63 62 64 62 60 61 66 64 61 65 in each graph class=
sixteen students each measured the weight of 25 pennies in grams the list shows their measurements 60 62 65 59 63 63 63 62 64 62 60 61 66 64 61 65 in each graph class=
sixteen students each measured the weight of 25 pennies in grams the list shows their measurements 60 62 65 59 63 63 63 62 64 62 60 61 66 64 61 65 in each graph class=
sixteen students each measured the weight of 25 pennies in grams the list shows their measurements 60 62 65 59 63 63 63 62 64 62 60 61 66 64 61 65 in each graph class=

Respuesta :

Answer:

Graph number 3.

Step-by-step explanation:

From the given data we will calculate the mean first

Mean = ∑Measurements/number of students = (60+62+65+59+63+63+63+62+64+62+60+61+66+64+61+65)/16 = 1000/16 = 62.5

Now to calculate standard deviation

Standard deviation = [tex]\sqrt{\frac{\sum (x-\bar{x})}{n-1}}[/tex]

[tex]=\sqrt{\frac{60}{15}}=\sqrt{4}=2[/tex]

So on the graph a solid vertical line should be at 62.5 and dotted vertical line segments will be at 60.5 and 64.5

The figure which matches our data is graph number 3.

Therefore Graph number 3 is the answer.

The graph third represents the distribution of weights if the mean of the data is 62.5 and the standard deviation is 2, the variation around the mean is 60.5 and 64.5

What is the standard deviation?

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

First, we have to find the mean of the data:

[tex]\rm Mean = \frac{\sum Measurements}{Total \ number \ of \ observation}[/tex]

[tex]\rm Mean = \frac{60+62+65+59+63+63+63+62+64+62+60+61+66+64+61+65}{16}[/tex]

[tex]\rm Mean = \frac{1000}{16}[/tex]

Mean = 62.5

Now finding standard deviation:

[tex]\rm SD = \sqrt{\frac{\sum (x-Mean)}{n-1} }[/tex]

[tex]\rm SD = \sqrt{\frac{60}{16-1} }[/tex]

[tex]\rm SD = \sqrt{\frac{60}{15} }[/tex]

SD = √4 ⇒ 2

Now taking variation around the mean

= 62.5-2 ⇒ 60.5

= 62.5+2 ⇒ 64.5

The vertical solid line should be at 62.5 and the dotted vertical line should be at 60.5 and 64.5

Thus, the graph third represents the distribution of weights if the mean of the data is 62.5 and the standard deviation is 2, the variation around the mean is 60.5 and 64.5

Learn more about the standard deviation here:

brainly.com/question/12402189

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