What value best represents all the measures of center for the following data set?
48, 12, 11, 45, 48, 48, 43, 32
2 (median) best describes the shape of the data set, as it is not skewed and the median is not heavily influenced by outliers.
The value that best represents all the measures of center for this data set is 45.
Use the table to answer the question.
Game Runs Scored
1 0
2 7
3 2
4 9
5 1
6 1
7 10
What value, the mean or the median, best describes the shape of the data set that contains the number of runs scored by the baseball team? Choose 1 for mean and 2 for median.
To find the value that best represents all the measures of center for the given data set, we need to calculate the mean, median, and mode.
Mean: The mean is calculated by summing all the values in the data set and dividing by the total number of values.
To find the mean, we add up all the numbers:
48 + 12 + 11 + 45 + 48 + 48 + 43 + 32 = 287
There are a total of 8 numbers in the data set, so we divide the sum by 8 to get the mean:
287 / 8 = 35.875
Therefore, the mean of the data set is approximately 35.875.
Median: The median is the middle value when the data set is arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.
First, let's arrange the values in ascending order:
11, 12, 32, 43, 45, 48, 48, 48
Since there are 8 values in the data set, the middle two values are the 4th and 5th numbers: 43 and 45. To find the median, we take the average of these two values:
(43 + 45) / 2 = 44
Therefore, the median of the data set is 44.
Mode: The mode is the value that appears most frequently in a data set. If there is no value that repeats, the data set is said to have no mode.
In the given data set, the value 48 appears three times, which is more than any other value. Therefore, the mode of the data set is 48.
In conclusion, the value that best represents all the measures of center for the given data set is:
Mean = 35.875
Median = 44
Mode = 48