In these set of data: 60,62,63,65,59,59,58,60,62,62,63,63,59,61,60,64,62,64,61,63 . Calculate the mean, mode, median, range, interquatile range, variance, standard deviation, and mean deviation
To calculate the mean, add up all the values and divide by the total number of values:
60 + 62 + 63 + 65 + 59 + 59 + 58 + 60 + 62 + 62 + 63 + 63 + 59 + 61 + 60 + 64 + 62 + 64 + 61 + 63 = 1210
Mean = 1210 / 20 = 60.5
To find the mode, identify the value(s) that appear the most frequently in the data set. In this case, the mode is 63, as it occurs 4 times, more frequently than any other value.
To calculate the median, arrange the data set in ascending order and find the middle value(s). In this case, the data set in ascending order is:
58, 59, 59, 59, 60, 60, 60, 61, 61, 62, 62, 62, 63, 63, 63, 64, 64, 65
The median is the middle value, which in this case is the 10th and 11th values: 61 and 62. To find the median, take the average of these two numbers:
Median = (61 + 62) / 2 = 61.5
To calculate the range, subtract the smallest value from the largest value:
Range = 65 - 58 = 7
To find the interquartile range, first find the first quartile (Q1) and third quartile (Q3). Since the data set has 20 values, the first quartile is the 5th value (60) and the third quartile is the 15th value (63). The interquartile range is the difference between these two values:
Interquartile Range = Q3 - Q1 = 63 - 60 = 3
To calculate the variance, first find the squared difference between each value and the mean, then sum up these squared differences, and divide by the total number of values:
(60 - 60.5)^2 + (62 - 60.5)^2 + (63 - 60.5)^2 + (65 - 60.5)^2 + (59 - 60.5)^2 + (59 - 60.5)^2 + (58 - 60.5)^2 + (60 - 60.5)^2 + (62 - 60.5)^2 + (62 - 60.5)^2 + (63 - 60.5)^2 + (63 - 60.5)^2 + (59 - 60.5)^2 + (61 - 60.5)^2 + (60 - 60.5)^2 + (64 - 60.5)^2 + (62 - 60.5)^2 + (64 - 60.5)^2 + (61 - 60.5)^2 + (63 - 60.5)^2 = 21.5
Variance = 21.5 / 20 ≈ 1.075
To calculate the standard deviation, take the square root of the variance:
Standard Deviation ≈ √1.075 ≈ 1.0376
To calculate the mean deviation, find the absolute difference between each value and the mean, sum up these absolute differences, and divide by the total number of values:
|60 - 60.5| + |62 - 60.5| + |63 - 60.5| + |65 - 60.5| + |59 - 60.5| + |59 - 60.5| + |58 - 60.5| + |60 - 60.5| + |62 - 60.5| + |62 - 60.5| + |63 - 60.5| + |63 - 60.5| + |59 - 60.5| + |61 - 60.5| + |60 - 60.5| + |64 - 60.5| + |62 - 60.5| + |64 - 60.5| + |61 - 60.5| + |63 - 60.5| = 21
Mean Deviation = 21 / 20 = 1.05