. Each week during the first half of the semester, a sample of 50 students was polled to
determine how many of them had their homework done before class. The following arc
the results of the weekly polls:
Week # # of students with homework done
1 1
2 8
3 12
4 14
5 22
6 30
7 25
8 8
a. Calculate the median.
b. Calculate the standard deviation.
a. Median is the 50th percentile.
b. 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
I'll let you do the calculations.
To calculate the median, follow these steps:
1. Arrange the data in ascending order:
1, 8, 12, 14, 22, 25, 30, 8
2. Determine the middle value(s) of the data set.
In this case, there are 8 data points, so we need to find the value in the middle. Since there is an even number of data points, we need to find the average of the two middle values. In this case, the middle values are the 4th and 5th data points: 14 and 22.
3. Calculate the median by taking the average of the two middle values:
Median = (14 + 22) / 2 = 36 / 2 = 18
So, the median is 18.
To calculate the standard deviation, follow these steps:
1. Calculate the mean (average) of the data set:
Mean = (1 + 8 + 12 + 14 + 22 + 25 + 30 + 8) / 8 = 120 / 8 = 15
2. Subtract the mean from each data point, square the result, and sum up the squared deviations:
(1 - 15)^2 + (8 - 15)^2 + (12 - 15)^2 + (14 - 15)^2 + (22 - 15)^2 + (25 - 15)^2 + (30 - 15)^2 + (8 - 15)^2 = 196 + 49 + 9 + 1 + 49 + 100 + 225 + 49 = 678
3. Divide the sum of squared deviations by the number of data points minus 1 (in this case, 8 - 1 = 7):
Variance = 678 / 7 = 96.857
4. Take the square root of the variance to obtain the standard deviation:
Standard Deviation = √96.857 ≈ 9.841
So, the standard deviation is approximately 9.841.