3. For a particular sample of 50 scores on a psychology exam, the following results were obtained.
Mean = 78 Mode = 84 Median = 80 Standard deviation = 11
1. What score was earned by more students than any other score? Why?
2. What is the variance?
To answer these questions, let's understand the concepts behind them and then use the given information to calculate the answers.
1. What score was earned by more students than any other score? Why?
The score earned by more students than any other score is called the mode. The mode represents the value in a dataset that occurs most frequently.
In our case, the given mode is 84. This means that more students earned a score of 84 than any other score in the sample. It could be because the exam had a question or questions that were relatively easier, resulting in more students getting that particular score.
2. What is the variance?
Variance is a measure of how spread out the scores are in a dataset. It quantifies the average squared deviation of the scores from the mean.
To calculate the variance, we can use the formula:
Variance = Sum of ((each score - mean) squared) / Total number of scores
Given that the mean of the sample is 78, and we have the scores, we can calculate the variance.
Step 1: Calculate the squared deviation of each score from the mean:
(84 - 78)^2 = 36
(80 - 78)^2 = 4
... (continue this calculation for each score)
Step 2: Sum up all the squared deviations:
36 + 4 + ... (continue this calculation for each squared deviation) = Total sum
Step 3: Divide the total sum by the total number of scores (50 in this case) to calculate the variance.
Let's perform these calculations to find the variance.
1. The mode of the sample is 84, which means that more students earned a score of 84 than any other score. This is because there are more 84s in the sample than any other score.
2. To find the variance, you can use the formula: variance = (standard deviation)^2.
In this case, the standard deviation is 11, so the variance would be:
variance = (11)^2 = 121.
Therefore, the variance for this sample of scores is 121.