Find the mean, median, and mode for the following
sample of scores:
8, 7, 8, 8, 4, 9, 10, 7, 8, 8, 9, 8
To find the mean, median, and mode for a set of scores, follow these steps:
Mean:
1. Add up all the scores in the sample: 8 + 7 + 8 + 8 + 4 + 9 + 10 + 7 + 8 + 8 + 9 + 8 = 96
2. Divide the sum by the total number of scores: 96 / 12 = 8
Therefore, the mean of the sample is 8.
Median:
1. Arrange the scores in ascending order: 4, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10
2. Since the sample size is even (12 in this case), take the average of the two middle scores: (8 + 8) / 2 = 8
Therefore, the median of the sample is 8.
Mode:
1. Identify which score(s) occur(s) most frequently in the sample.
In this case, the score of 8 appears the most frequently (5 times), while the other scores appear less frequently.
Therefore, the mode of the sample is 8.
To find the mean, median, and mode, follow these steps:
Step 1: Arrange the scores in ascending order:
4, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10
Step 2: Calculate the mean:
To find the mean, add up all the numbers and then divide by the total number of scores:
4 + 7 + 7 + 8 + 8 + 8 + 8 + 8 + 9 + 9 + 10 = 96
Mean = 96 / 11 = 8.7273 (rounded to four decimal places)
Step 3: Calculate the median:
The median is the middle value in a set of data when it is arranged in ascending order.
Since there are 11 scores, the median will be the value at the (11 + 1) / 2 = 6th position.
In this case, the 6th value is 8.
Step 4: Calculate the mode:
The mode is the score that appears most frequently in the data set.
In this case, the score that appears most frequently is 8.
So, the mean is approximately 8.7273, the median is 8, and the mode is 8.