Certainly! Let's analyze Jamie's five recent bowling scores which are 85, 78, 65, 90, and 65. We'll calculate and compare the range, mean, median, and mode to determine which measure has the greatest value.
### Range
The range is calculated by subtracting the smallest score from the largest score:
- Largest score = 90
- Smallest score = 65
Therefore, the range:
[tex]\[ \text{Range} = 90 - 65 = 25 \][/tex]
### Mean
The mean (or average) is found by summing all the scores and dividing by the number of scores:
Sum of the scores:
[tex]\[ 85 + 78 + 65 + 90 + 65 = 383 \][/tex]
Number of scores:
[tex]\[ 5 \][/tex]
Thus, the mean:
[tex]\[ \text{Mean} = \frac{383}{5} = 76.6 \][/tex]
### Median
The median is the middle value when the scores are arranged in ascending order. First, let's sort the scores:
[tex]\[ 65, 65, 78, 85, 90 \][/tex]
Since there are 5 scores, the median is the third number in this sorted list:
[tex]\[ \text{Median} = 78 \][/tex]
### Mode
The mode is the number that appears most frequently in the list of scores. Let's identify the frequencies of each score:
- 65 appears 2 times
- 85 appears 1 time
- 78 appears 1 time
- 90 appears 1 time
Since 65 appears most frequently, the mode:
[tex]\[ \text{Mode} = 65 \][/tex]
### Comparison of Measures
To summarize:
- Range: 25
- Mean: 76.6
- Median: 78
- Mode: 65
Among the range, mean, median, and mode, the mean has the greatest value, which is 76.6.
So, the statistical measures for Jamie's bowling scores are:
- Range: 25
- Mean: 76.6
- Median: 78
- Mode: 65
The measure with the greatest value is the mean, which is 76.6.
