Q1 = 3, Q3 = 9; IQR = Q3 - Q1 = 9 - 3 = 6.
Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.
Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.
Mean = 5, Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.
Mean = (4+8+6+5+3)/5 = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 2.5.
Range = Maximum - Minimum = 30 - 10 = 20.
Mean = 30; Mean Deviation = (|10-30| + |20-30| + |30-30| + |40-30| + |50-30|) / 5 = 10.
The mode is the number that appears most frequently, which is 23.
There is no mode as all values appear only once.
Mean = 6; Mean deviation = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|)/5 = (4 + 2 + 0 + 2 + 4)/5 = 12/5 = 2.4.
Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.0.
Q1 = 2, Q3 = 4; Interquartile Range = Q3 - Q1 = 4 - 2 = 2.
Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.
Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41
Since the mean is greater than the median, the data is positively skewed.
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.
Standard Deviation = √Variance = √16 = 4.
Since the mean is greater than the median, the distribution is positively skewed.
Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.
Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.
Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.
Median = (7 + 7) / 2 = 7.
Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.
The standard deviation remains the same because the transformation is a shift.
Standard deviation remains the same as adding a constant does not affect dispersion.
Q1 is the median of the first half of the data set {3, 7}, which is 7.
Median is the middle value, which is 8.
The sum of deviations from the mean is always 0.
