Question

1. you want a test average of 85. your first five test scores were 86, 80, 77, 81, and 89. what score do you need to earn on the final to get the test average you are looking for?
2. the following data set shows the hours of time spent on tiktok for a group of freshmen: 10, 12, 20, 22, 23, 24, 26, 29, 29, 32, 38, 40, 42, 42

(a) determine the five - number summary and iqr. (__, , , , __) iqr
(b) calculate whether there are any outliers. show work below
list outliers here, if any: ____________
(c) make a well labeled box - plot below
(d) find each of the following: mean: mode: range: standard deviation:

Explanation:

Step1: Calculate sum of first five scores

$86 + 80+77 + 81+89=413$

Step2: Set up average - formula equation

Let the final score be $x$. The average of six scores is $\frac{413 + x}{6}$, and we want this to be 85. So, $\frac{413+x}{6}=85$.

Step3: Solve the equation for $x$

Multiply both sides of the equation by 6: $413 + x=85\times6 = 510$. Then subtract 413 from both sides: $x=510 - 413=97$.

for question 6(a):

Step1: Arrange data in ascending order

The data set is already in ascending order: $10,12,20,22,23,24,26,29,29,32,38,40,42,42$.

Step2: Find the minimum

The minimum value is 10.

Step3: Find the first - quartile ($Q_1$)

There are $n = 14$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{14+1}{4}=3.75$. So, $Q_1=20+(22 - 20)\times0.75 = 21.5$.

Step4: Find the median

The position of the median is $\frac{n+1}{2}=\frac{14 + 1}{2}=7.5$. So, the median is $\frac{26+29}{2}=27.5$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(14 + 1)}{4}=11.25$. So, $Q_3=32+(38 - 32)\times0.25=33.5$.

Step6: Find the maximum

The maximum value is 42.

Step7: Calculate the IQR

$IQR=Q_3 - Q_1=33.5-21.5 = 12$.

for question 6(b):

Step1: Calculate the lower and upper bounds for non - outliers

The lower bound is $Q_1-1.5\times IQR=21.5-1.5\times12=21.5 - 18 = 3.5$. The upper bound is $Q_3+1.5\times IQR=33.5+1.5\times12=33.5 + 18=51.5$.

Step2: Check for outliers

Since all the data values ($10,12,20,22,23,24,26,29,29,32,38,40,42,42$) are between 3.5 and 51.5, there are no outliers.

for question 6(d):

Step1: Calculate the mean

$\text{Mean}=\frac{10 + 12+20+22+23+24+26+29+29+32+38+40+42+42}{14}=\frac{369}{14}\approx26.36$.

Step2: Calculate the mode

The mode is 29 and 42 (both appear twice).

Step3: Calculate the range

The range is $42-10 = 32$.

Step4: Calculate the standard deviation

First, find the squared differences from the mean for each data point. Then find the average of these squared differences (the variance), and then take the square - root of the variance.
The variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n-1}$.
$\sum_{i = 1}^{14}(x_i - 26.36)^2=(10 - 26.36)^2+(12 - 26.36)^2+\cdots+(42 - 26.36)^2$.
$=( - 16.36)^2+( - 14.36)^2+\cdots+(15.64)^2$
$=267.6496+206.2096+\cdots+244.6096$.
$\sum_{i = 1}^{14}(x_i - 26.36)^2 = 1779.7144$.
The variance $s^{2}=\frac{1779.7144}{13}\approx136.9011$.
The standard deviation $s=\sqrt{136.9011}\approx11.70$.

Answer:

97