In a carnival game, players get 5 chances to

Question

throw a basketball through a hoop. The dot
plot shows the number of baskets made by
20 different players.
a. Make an inference by looking at the shape of
the data.
b. What is the median of the data? What is the
mean? Do these measures of center support
the inference you made in part (a)?

Answer 1

To provide an accurate analysis, I would need to see the dot plot data showing the number of baskets made by the 20 different players. Since I cannot view images, I'll guide you on how to analyze the data based on general principles.

a. Inference from the Shape of the Data

1. Shape of Data: Look for the distribution of the data points in the dot plot.

   • If the dots cluster around a certain number, it suggests that most players achieved that number of baskets.
   • If the data skews to one side, it might indicate that fewer players were able to score high or low.
   • A bell-shaped curve would suggest a normal distribution, while a skewed plot could indicate an asymmetric distribution.

2. Inference Examples:

   • If most players made 3 or 4 baskets, you might infer that the skill level of the players is moderate.
   • If the data has a long tail towards 5, you might infer that there are some particularly skilled players.
   • If most players made 1 or 2 baskets with a few outliers making 5, you might infer that the game is challenging.

b. Calculating the Median and Mean

1. Median:

   • To find the median, arrange the number of baskets in numerical order. For 20 players (an even number), the median will be the average of the 10th and 11th numbers in the sorted list.

2. Mean:

   • To calculate the mean, add up all the baskets made and divide by the number of players (20).

Analysis of Measures of Center:

• Once you calculate the median and mean, compare the two:
  • Median vs. Mean:
    • If the mean is significantly higher than the median, it indicates a right skew (a few players scored much higher) which might support the inference of a few skilled players.
    • If the median is higher than the mean, it suggests a left skew (more players scored lower), indicating that most players had difficulty with the game.

Conclusion:

• By looking at the shapes, the median, and mean, you can confirm or refute your initial inference from the dot plot. The measures of center support the conclusions drawn based on how players performed in the game.

If you have specific data points or further details from the dot plot, I would be glad to provide more tailored assistance!