Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The table below shows data from a survey about the amount of time students spend doing homework each week. The students were in either college or high school:

\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
& High & Low & Q1 & Q3 & IQR & Median & Mean & [tex]$\sigma$[/tex] \\
\hline
College & 50 & 6 & 8.5 & 17 & 8.5 & 12 & 15.4 & 11.7 \\
\hline
High School & 28 & 3 & 4.5 & 15 & 10.5 & 11 & 10.5 & 5.8 \\
\hline
\end{tabular}

Which of the choices below best describes how to measure the spread of these data?

A. Both spreads are best described by the IQR.
B. Both spreads are best described by the standard deviation.
C. The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D. The college spread is best described by the standard deviation. The high school spread is best described by the IQR.

Sagot :

GinnyAnswer
Given the data:
- High School: Minimum = 3, Maximum = 28, Q1 = 4.5, Q3 = 15, IQR = 10.5, Median = 11, Mean = 10.5, Sigma = 5.8
- College: Minimum = 6, Maximum = 50, Q1 = 8.5, Q3 = 17, IQR = 8.5, Median = 12, Mean = 15.4, Sigma = 11.7

We'll follow these steps to determine the best measure of spread:

### Step 1: Calculate the Range for Each Dataset
The range is calculated as the difference between the maximum and minimum values.

- High School Range:
[tex]\[ 28 - 3 = 25 \][/tex]

- College Range:
[tex]\[ 50 - 6 = 44 \][/tex]

### Step 2: Determine Interquartile Range (IQR)
IQR is given directly in the data:
- High School IQR: 10.5
- College IQR: 8.5

### Step 3: Check for Potential Outliers
Outliers can influence whether mean and standard deviation are appropriate, or if the IQR should be used instead.

- High School Data Check for Outliers:
[tex]\[ \text{Potential high outlier if } \text{Mean} > \text{Q3} + 1.5 \times \text{IQR} \quad (\text{or}) \][/tex]
[tex]\[ \text{Potential low outlier if } \text{Mean} < \text{Q1} - 1.5 \times \text{IQR} \][/tex]

[tex]\[ \text{Q3} + 1.5 \times \text{IQR} = 15 + 1.5 \times 10.5 = 30.75 \quad (\text{Mean} = 10.5 \leq 30.75) \][/tex]
[tex]\[ \text{Q1} - 1.5 \times \text{IQR} = 4.5 - 1.5 \times 10.5 = -11.25 \quad (\text{Mean} = 10.5 \geq -11.25) \][/tex]

Since both conditions are not met, there are no apparent outliers in the high school data.

- College Data Check for Outliers:
[tex]\[ \text{Q3} + 1.5 \times \text{IQR} = 17 + 1.5 \times 8.5 = 29.75 \quad (\text{Mean} = 15.4 \leq 29.75) \][/tex]
[tex]\[ \text{Q1} - 1.5 \times \text{IQR} = 8.5 - 1.5 \times 8.5 = -4.25 \quad (\text{Mean} = 15.4 \geq -4.25) \][/tex]

Similar to the high school data, these conditions imply there are no apparent outliers.

### Step 4: Determine Best Measure of Spread
With the absence of significant outliers, the interquartile range (IQR) is a suitable measure of spread for both datasets as the data is relatively symmetrically distributed.

### Conclusion
Therefore, the best measure of spread for both the high school and college data is the IQR.

Answer: Both spreads are best described by the IQR.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.