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Find the mean, mode, range, median, vanance, standard deviation of the following data 1 The data represent the number of meals purchased during one night's business at a restaurant 153 104 118 166 89 104 100 79 93 96 11694 140 84 81 86 108 111 87 126 101 111 122 108 126 93 108 87 103 95 129 93

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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

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