Answer: Mean ≈ 105.81
Mode = No mode
Range = 87
Median = 104
Variance ≈ 924.35
Standard Deviation ≈ 30.40
Explanation:
To find the mean, mode, range, median, variance, and standard deviation of the given data, let's calculate each one step by step:
Mean:
To find the mean, we sum up all the values and divide by the total number of values.
Mean = (153 + 104 + 118 + 166 + 89 + 104 + 100 + 79 + 93 + 96 + 116 + 94 + 140 + 84 + 81 + 86 + 108 + 111 + 87 + 126 + 101 + 111 + 122 + 108 + 126 + 93 + 108 + 87 + 103 + 95 + 129 + 93) / 31
Mean = 3,280 / 31
Mean ≈ 105.81
Mode:
The mode is the value(s) that appears most frequently in the data.
In this case, there is no value that appears more than once. Therefore, there is no mode.
Range:
The range is the difference between the maximum and minimum values in the data.
Range = Maximum value - Minimum value
Range = 166 - 79
Range = 87
Median:
To find the median, we arrange the data in ascending order and find the middle value.
Arranging the data in ascending order: 79, 81, 84, 86, 87, 87, 89, 93, 93, 94, 95, 96, 100, 101, 103, 104, 104, 108, 108, 111, 111, 116, 118, 122, 126, 126, 129, 140, 153, 166
Since the data set has 31 values, the median will be the 16th value.
Median = 104
Variance:
To find the variance, we need to calculate the squared difference between each data point and the mean, sum up those squared differences, and divide by the total number of values.
Variance = Σ((x - mean)²) / n
where Σ represents the sum, x represents each data point, mean is the mean value, and n is the total number of values.
Calculating the variance:
Variance = ((153 - 105.81)² + (104 - 105.81)² + ... + (93 - 105.81)²) / 31
Variance ≈ 924.35
Standard Deviation:
The standard deviation is the square root of the variance.
Standard Deviation ≈ √924.35
Standard Deviation ≈ 30.40