1. The exam scores for the students in an introductory statistics class are as follows.
88 63 90 64 82 98 96 75 89 86 76
84 70 67 34 89 85 39 81 96 92 85
a. Compute the mean and the median score.
b. Identify the shape of the distribution of score. Explain why.
c. Construct a frequency distribution using 6 classes of equal width.
d. Use midpoints of the classes to compute average score.
I don't Understand
To find the mean score, you need to add up all the scores and then divide by the total number of scores. To find the median score, you need to arrange the scores in ascending order and then find the middle score.
a. To compute the mean score:
- Add up all the scores: 88+63+90+64+82+98+96+75+89+86+76+84+70+67+34+89+85+39+81+96+92+85
- Divide the sum by the total number of scores (which is 22 in this case).
b. To identify the shape of the distribution, you can create a histogram or examine the data to make an assessment. However, based on the scores given, it is difficult to determine the exact shape of the distribution. It is unclear whether the data is normally distributed, skewed, or has other characteristics. More information or a visual representation would be required to identify the shape of the distribution.
c. To construct a frequency distribution using 6 classes of equal width, you need to determine the range of the data and divide it into 6 equal intervals.
- Find the range by subtracting the smallest value from the largest value.
- Divide the range by the number of desired classes (6) to determine the width of each class.
- Start with the smallest value and create intervals with the determined width until you reach the largest value. Count the number of scores falling within each interval.
d. To use midpoints of the classes to compute the average score:
- Determine the midpoint of each class interval by adding the lower and upper limits of each class and dividing by 2.
- Multiply each midpoint by the frequency of scores in that interval.
- Add up all the products and divide by the total number of scores (which is 22 in this case).
Note: The steps provided are general explanations of how to solve the problem. If you want to see the exact calculations, please provide the range and the number of classes for the frequency distribution.