The number of days absent was recorded for a sample of 10 students. Here are the data:
7,2,6,7,4,2,0,6,10,8
Find each of these statistics for this data set. Round your answers to two decimal places, if necessary.
Sample Mean
Sample Median
Sample Range
Sample Standard Deviation
Interquartile Range
Sample Mean:
(7+2+6+7+4+2+0+6+10+8)/10 = 5.2
Sample Median:
Arrange the data in increasing order: 0,2,2,4,6,6,7,7,8,10
Since there are 10 values, the median is the average of the 5th and 6th values: (6+6)/2 = 6
Sample Range:
Range = maximum value - minimum value
Range = 10-0 = 10
Sample Standard Deviation:
Calculate the variance first:
Step 1: Calculate the mean (already calculated above): 5.2
Step 2: Subtract the mean from each data point and square the result:
(7-5.2)^2 = 3.24
(2-5.2)^2 = 9.61
(6-5.2)^2 = 0.64
(7-5.2)^2 = 3.24
(4-5.2)^2 = 1.44
(2-5.2)^2 = 9.61
(0-5.2)^2 = 27.04
(6-5.2)^2 = 0.64
(10-5.2)^2 = 23.04
(8-5.2)^2 = 7.84
Step 3: Calculate the variance by summing all the squared differences and dividing by n-1:
(3.24+9.61+0.64+3.24+1.44+9.61+27.04+0.64+23.04+7.84)/9 = 7.8902
Step 4: Calculate the standard deviation by taking the square root of the variance:
√7.8902 ≈ 2.81
Interquartile Range:
Arrange the data in increasing order: 0,2,2,4,6,6,7,7,8,10
Q1 = 2
Q3 = 7
Interquartile Range = Q3 - Q1 = 7-2 = 5