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1.)The data shows the number of grams of fat found in 9 different health bars.

12, 14, 16, 17.5, 10, 18, 15, 15.5, 19

What is the IQR (interquartile range) for the data?



4.75

9

15.5

17.75

2.) What is the range of the data set?

32, 21, 88, 64, 88, 107, 101

3.) Lara is calculating the standard deviation of a data set that has 8 values. She determines that the sum of the squared deviations is 184.


What is the standard deviation of the data set?
 

Round the answer to the nearest tenth.

4.) What is the standard deviation of the data set?


7, 3, 4, 2, 5, 6, 9

Round the answer to the tenths place.

 

2.45.05.15.8

Respuesta :

boffeemadrid

Answer:

Step-by-step explanation:

1. The given data is:

12, 14, 16, 17.5, 10, 18, 15, 15.5, 19

Arrange this in ascending order, we have

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

The median of the given data is 15.5, thus the lower quartile is:

[tex]LQ=\frac{12+14}{2}=\frac{26}{2}=13[/tex] and

Upper quartile is:

[tex]UQ=\frac{17.5+18}{2}=\frac{35.5}{2}=17.75[/tex]

Now, the interquartile range is given as:

[tex]IQR=UQ-LQ[/tex]

[tex]IQR=17.75-13=4.75[/tex]

Option A is correct.

2. The given data set is:

32, 21, 88, 64, 88, 107, 101

Now, the range is given as:

[tex]Range=highestvalue-lowest value[/tex]

[tex]Range=107-21=86[/tex]

3. It is given that  Lara is calculating the standard deviation of a data set that has 8 values. She determines that the sum of the squared deviations is 184.

Thus, Number of data=8 and sum of squared deviations=184

Now, [tex]variance=\frac{Sum of squared deviation}{no. of data}[/tex]

[tex]V=\frac{184}{8}=23[/tex]

Thus, [tex]SD=\sqrt{23}=4.8[/tex]

4. The given data set is:

7, 3, 4, 2, 5, 6, 9

[tex]Mean=\frac{7+3+4+2+5+6+9}{7}[/tex]

[tex]Mean=5.14[/tex]

Now, find the distance of mean from each data point, we have

Data points                                                  [tex](x-\overline{x})^2[/tex]

7                                                                            3.45

3                                                                            4.57

4                                                                            1.29

2                                                                            9.85

5                                                                            0.01

6                                                                            0.73

9                                                                           14.89

Now, [tex](x-\overline{x})^2=3.45+4.57+1.29+9.85+0.01+0.73+14.89=34.79[/tex]

Then, [tex]\frac{(x-\overline{x})^2}{7}=\frac{34.79}{7}=4.97[/tex]

Thus, standard deviation is:

[tex]SD=\sqrt{4.97}[/tex]

[tex]SD[/tex]≈[tex]2.4[/tex]

Based on the information given, the value of the interquartile range will be 4.75.

  • From the information, the first thing to do is to arrange the data in ascending order. This will be: 10, 12, 14, 15, 15.5, 16, 17.5, 18, and 19.

  • The median in this case is 15.5.

The lower quartile will be:

= (12 + 14)/2

= 26/2 = 13

The upper quartile will be:

= (17.5 + 18)/2 = 17.75

Therefore, the interquartile range will be:

= Upper quartile - Lower quartile

= 17.75 - 13 = 4.75

From the given numbers, the range of the data set from 32, 21, 88, 64, 88, 107, 101 will be:

= Highest number - Lowest number

= 107 - 21 = 86

Since the sum of the squared deviations is 184 and the number of data is 8, the variance will be:

= 184/8 = 23

Therefore, the standard deviation will be the square root of 23 which is 4.8

Lastly, the mean of the data set 7, 3, 4, 2, 5, 6, 9 is 5.14. The summation of the distance of the mean from each point will be 4.97.

Therefore, the standard deviation will be:

= ✓4.97

= 2.4

Learn more about standard deviation on:

https://brainly.com/question/19243813

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