Miss C gives a test to the 10 students in her first-period algebra class. The grades are
93,82,95,86,90,84,89,79,87,93
A. Find the mean and Standard Deviation of the 10 scores.
B. List all the reasons for why the late class could have a different mean or standard deviation
A. Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
B. Inadequate data
I'll let you do the calculations.
To find the mean and standard deviation of the given scores, follow these steps:
A. Finding the mean:
1. Add up all the scores: 93 + 82 + 95 + 86 + 90 + 84 + 89 + 79 + 87 + 93 = 878.
2. Divide the sum by the total number of scores (10 in this case): 878 / 10 = 87.8.
The mean of the scores is 87.8.
B. Finding the standard deviation:
1. Calculate the deviation of each score from the mean by subtracting the mean from each score. For example:
Deviation for score 1 = 93 - 87.8 = 5.2
Deviation for score 2 = 82 - 87.8 = -5.8
Deviation for score 3 = 95 - 87.8 = 7.2
...
2. Square each deviation:
Squared deviation for score 1 = 5.2^2 = 27.04
Squared deviation for score 2 = (-5.8)^2 = 33.64
Squared deviation for score 3 = 7.2^2 = 51.84
...
3. Calculate the average of the squared deviations by adding them up and dividing by the total number of scores:
(27.04 + 33.64 + 51.84 + ...) / 10 = sum of squared deviations / 10
4. Take the square root of the average of the squared deviations to find the standard deviation.
Now, addressing the second part of your question:
B. There are several reasons why the late class could have a different mean or standard deviation:
1. Difference in student performance: The late class might have different levels of understanding, resulting in variations in scores and thus affecting both the mean and standard deviation.
2. Different teaching style or methods: The teacher for the late class might have a different approach or different emphasis on certain topics, leading to variations in student scores.
3. Sample size: If the late class has significantly fewer or more students than Miss C's class, this could affect the mean and standard deviation. A smaller sample size generally leads to more variability in the results.
4. Random chance: The distribution of scores in the late class might be influenced by random chance, resulting in different mean and standard deviation values compared to Miss C's class.
It's important to analyze these factors to understand why the late class might have different mean and standard deviation values.