Question

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

Answer 1

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:

$LQ=\frac{12+14}{2}=\frac{26}{2}=13$ and

Upper quartile is:

$UQ=\frac{17.5+18}{2}=\frac{35.5}{2}=17.75$

Now, the interquartile range is given as:

$IQR=UQ-LQ$

$IQR=17.75-13=4.75$

Option A is correct.

2. The given data set is:

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

Now, the range is given as:

$Range=highestvalue-lowest value$

$Range=107-21=86$

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, $variance=\frac{Sum of squared deviation}{no. of data}$

$V=\frac{184}{8}=23$

Thus, $SD=\sqrt{23}=4.8$

4. The given data set is:

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

$Mean=\frac{7+3+4+2+5+6+9}{7}$

$Mean=5.14$

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

Data points                                                  $(x-\overline{x})^2$

7                                                                            3.45

3                                                                            4.57

4                                                                            1.29

2                                                                            9.85

5                                                                            0.01

6                                                                            0.73

9                                                                           14.89

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

Then, $\frac{(x-\overline{x})^2}{7}=\frac{34.79}{7}=4.97$

Thus, standard deviation is:

$SD=\sqrt{4.97}$

$SD$≈$2.4$

Answer 2

Given:

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

The IQR of the data is determined by first arranging the data according to their values, from lowest to highest:

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19
 
IQR = 4.75 = Q3 - Q1

What is the range of the data set?

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

Again, rearrange the data according to value (lowest to highest), then find the minimum and maximum values:

Range = 21 to 107