It seems like you have uploaded an image with data. Let me first extract and analyze the MPG data in the table to proceed with the calculations.

I will retrieve the data and solve the given questions:

1. a) Compute the z-score for the individual who obtained 48.8 miles per gallon.
2. b) Determine the quartiles.
3. c) Compute and interpret the interquartile range (IQR).
4. d) Determine the lower and upper fences. Are there any outliers?

Let me first analyze and extract the data from the image. PIL import Image

Load the image to inspect it

img_path = '/mnt/data/1741172234182cyrtiq3a.jpg' img = Image.open(img_path)

Display the image to understand its content

img.show()I have opened the image, but I'll need to extract the data more clearly to perform the necessary calculations. Let me process the data from the image and move forward with the questions. pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(img)

extracted_textI successfully extracted the data from the image. The values for miles per gallon (MPG) are:

• 32.7, 36.3, 37.8, 38.5, 40.3, 42.6
• 34.5, 36.4, 38.0, 39.1, 40.6, 42.8
• 34.6, 37.3, 38.2, 39.5, 41.4, 43.4
• 35.8, 37.6, 38.4, 39.7, 41.7, 48.8

Now I will proceed to solve the questions you mentioned.

Part (a): Compute the z-score for the individual who obtained 48.8 miles per gallon

To calculate the z-score, we need to first find the mean and standard deviation of the dataset.

The formula for the z-score is:

$z = \frac{{X - \mu}}{{\sigma}}$

Where:

• $X$ is the value of interest (48.8 in this case),
• $\mu$ is the mean of the dataset,
• $\sigma$ is the standard deviation of the dataset.

Let's calculate these values now. numpy as np

MPG data extracted from the image

mpg_data = np.array([32.7, 36.3, 37.8, 38.5, 40.3, 42.6, 34.5, 36.4, 38.0, 39.1, 40.6, 42.8, 34.6, 37.3, 38.2, 39.5, 41.4, 43.4, 35.8, 37.6, 38.4, 39.7, 41.7, 48.8])

Calculate mean and standard deviation

mean_mpg = np.mean(mpg_data) std_dev_mpg = np.std(mpg_data)

Compute the z-score for 48.8

x_value = 48.8 z_score = (x_value - mean_mpg) / std_dev_mpg

mean_mpg, std_dev_mpg, z_scoreThe mean of the MPG data is 39.0, and the standard deviation is approximately 3.37.

The z-score for the individual who obtained 48.8 miles per gallon is approximately 2.91.

Interpretation:

This z-score indicates that the value of 48.8 MPG is 2.91 standard deviations above the mean. This suggests that the value is significantly higher than most of the data points in the sample.

Part (b): Determine the quartiles

The quartiles are values that divide the data into four equal parts:

• Q1 (lower quartile): The median of the lower half of the data.
• Q2 (median): The middle value of the dataset.
• Q3 (upper quartile): The median of the upper half of the data.

Let me calculate the quartiles for you. Calculate the quartiles Q1 = np.percentile(mpg_data, 25) Q2 = np.percentile(mpg_data, 50) # Median Q3 = np.percentile(mpg_data, 75)

Q1, Q2, Q3It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any other questions or need assistance with a different topic, feel free to ask!