Question
Use the table to answer the question. This table shows the number of free throws made by the basketball team in each game. Game Free Throws Made 1 4 2 14 3 5 4 7 5 19 6 15 7 6 What value, the mean or median, best describes the shape of the data set that contains the number of free throws made by the basketball team? Choose 1 for mean and 2 for median. (1 point)
Answers
GPT-4o mini
To determine whether the mean or median best describes the shape of the data set, we should first calculate both the mean and the median of the free throws made by the basketball team.
**Free Throws Made (in order):** 4, 5, 6, 7, 14, 15, 19
**Calculating the Mean:**
Mean = (Sum of all values) / (Number of values)
\(4 + 5 + 6 + 7 + 14 + 15 + 19 = 70\)
Number of games = 7
Mean = \(70 / 7 = 10\)
**Calculating the Median:**
To find the median, we first order the data (which is already done) and then find the middle value. Since there are 7 values (an odd number), the median is the middle value:
- The middle value (4th value) is **7**.
**Summary:**
- Mean = 10
- Median = 7
Now we can look at the shape of the data: the data set has a few low scores and one very high score (19). This may cause the mean to be skewed higher than the median.
Since the mean (10) is greater than the median (7), the mean is influenced by the high value.
Therefore, in this case, the median (7) would be a better representation of the data because it is less affected by the outlier and more indicative of the central tendency of the majority of the data.
So, the answer is **2 (median)**.
**Free Throws Made (in order):** 4, 5, 6, 7, 14, 15, 19
**Calculating the Mean:**
Mean = (Sum of all values) / (Number of values)
\(4 + 5 + 6 + 7 + 14 + 15 + 19 = 70\)
Number of games = 7
Mean = \(70 / 7 = 10\)
**Calculating the Median:**
To find the median, we first order the data (which is already done) and then find the middle value. Since there are 7 values (an odd number), the median is the middle value:
- The middle value (4th value) is **7**.
**Summary:**
- Mean = 10
- Median = 7
Now we can look at the shape of the data: the data set has a few low scores and one very high score (19). This may cause the mean to be skewed higher than the median.
Since the mean (10) is greater than the median (7), the mean is influenced by the high value.
Therefore, in this case, the median (7) would be a better representation of the data because it is less affected by the outlier and more indicative of the central tendency of the majority of the data.
So, the answer is **2 (median)**.