Let's analyze the data step by step to find the correct values for the mean, median, and standard deviation of the number of homework nights.

Step 1: Mean Calculation

The mean is calculated by summing all values and dividing by the total number of values.

1. List all the data points from the image (survey results):

   5, 3, 4, 5, 4, 3, 6, 1, 5, 3,
   7, 4, 4, 6, 2, 3, 7, 3, 6, 6,
   5, 7, 2, 5, 2, 5, 1, 1, 6, 6,
   5, 7, 5, 5, 2, 1, 5, 3, 1, 6,
   7, 4, 5, 5, 3, 5, 1, 4, 1, 7,
   7, 4, 5, 3, 4, 6, 2, 6, 2, 7
   

2. Sum these values: $\text{Sum} = 5 + 3 + 4 + \ldots + 7 = 256$

3. Divide by the number of data points (60): $\text{Mean} = \frac{256}{60} \approx 4.27$

Step 2: Median Calculation

To find the median, the data should be sorted, and the middle value located. For 60 data points, the median will be the average of the 30th and 31st values.

1. Sort the dataLet's analyze the data step by step to find the correct values for the mean, median, and standard deviation of the number of homework nights.

Step 1: Mean Calculation

The mean is calculated by summing all values and dividing by the total number of values.

1. List all the data points from the image (survey results):

   5, 3, 4, 5, 4, 3, 6, 1, 5, 3,
   7, 4, 4, 6, 2, 3, 7, 3, 6, 6,
   5, 7, 2, 5, 2, 5, 1, 1, 6, 6,
   5, 7, 5, 5, 2, 1, 5, 3, 1, 6,
   7, 4, 5, 5, 3, 5, 1, 4, 1, 7,
   7, 4, 5, 3, 4, 6, 2, 6, 2, 7
   

2. Sum these values: $\text{Sum} = 5 + 3 + 4 + \ldots + 7 = 256$

3. Divide by the number of data points (60): $\text{Mean} = \frac{256}{60} \approx 4.27$

Step 2: Median Calculation

To find the median, the data should be sorted, and the middle value located. For 60 data points, the median will be the average of the 30th and 31st values.

1. Sort the

   1, 1, 1, 1, 1, 1, 1, 2, 2, 2,
   2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
   4, 4, 4, 4, 4, 4, 4, 5, 5, 5,
   5, 5, 5, 5, 5, 5, 5, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7
   

2. The 30th and 31st values are both 4, so the median is: $\text{Median} = 4.00$

Step 3: Standard Deviation Calculation

Use the formula for sample standard deviation: $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$ Where:

• $x_i$ are the data points
• $\bar{x}$ is the mean
• $n$ is the number of data points

1. Calculate the squared deviations from the mean (4.27): $(5-4.27)^2, (3-4.27)^2, \ldots, (7-4.27)^2$

2. Sum these squared deviations and divide by 59 (n-1): $\text{Sum of squared deviations} \approx 201.29$

3. Find the standard deviation: $s = \sqrt{\frac{201.29}{59}} \approx 1.85$

Summary:

• Mean: 4.27
• Median: 4.00
• Standard Deviation: 1.85

Do you need further details, or have any questions?

1. How can calculating the mean help in understanding a dataset?
2. What is the difference between population and sample standard deviation?
3. Why is it important to use (n-1) for the sample standard deviation?
4. How does the median help to understand the skewness of the data?
5. What effect would an outlier have on the mean and standard deviation?

Tip: Always double-check if you are using population or sample formulas when computing statistics.