To determine which statement does NOT describe the given set of data, let's analyze each step-by-step:
1. Finding the Mode:
- The mode of a set of data is the value that appears most frequently.
- In the given test scores: 76, 76, 72, 100, and 75, the number 76 appears twice, which is more often than any other number.
- Therefore, the mode is 76.
Statement A) The mode is 76 - This is correct.
2. Calculating the Mean:
- The mean (average) is calculated by adding all the scores together and dividing by the number of scores.
- Sum of scores: [tex]\( 76 + 76 + 72 + 100 + 75 = 399 \)[/tex]
- Number of scores: 5
- Mean: [tex]\( \frac{399}{5} = 79.8 \)[/tex]
Statement B) The mean is greater than the median - We need to calculate the median to verify this statement.
3. Finding the Median:
- The median is the middle value in a list of numbers ordered from smallest to largest.
- Ordered scores: 72, 75, 76, 76, 100
- The middle value (since there are five scores) is the third score, which is 76.
Statement C) The median is 72 - This is incorrect because the median is actually 76.
4. Comparing Mode and Median:
- From our calculations, both the mode and the median are 76.
Statement D) The mode and the median are equal - This is correct as both are 76.
Now that we have analyzed all the statements:
- Statement A is correct.
- Statement B is correct, as the mean (79.8) is indeed greater than the median (76).
- Statement C is incorrect, because the median is 76, not 72.
- Statement D is correct.
The statement that does NOT describe the set of data is:
C) The median is 72.
