Question #1), Calculate the mean, median, mode, and range for the following sales data 1700; 2200; 2400; 2900; 1800; 3700; 1200; 2300; 600; 1600; 2000; 3900; 1100; 1700; 2900; 2900; $2900. Question #2), Calculate the mean, median, mode, range, variance, and standard deviation for the following dataset: 8; 2; 4; 0; 1; 3; 5; 10; 6; 11; 12; 3; 9; 7; 3; 8; 12; 14; 16; 18; 21 Question 3) Identify the outliers in the dataset below 2037242899801202231 53416429 Question 4), Calculate the median, the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3), and identify all outliers in the dataset below. Please show the steps leading to your answers. 180250025540015691761631827166 171 Question 5) If Q1 = 5 and Q3 = 15, find the interquartile range and locate the lower and upper fences.

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Asked on June 23, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-06-23T19:49:54.340Z

Here are the calculations for your questions. Question #1) Calculate the mean, median, mode, and range for the following sales data: 1700; 2200; 2400; 2900; 1800; 3700; 1200; 2300; 600; 1600; 2000; 3900; 1100; 1700; 2900; 2900; 2900. Step 1: Order the data. First, arrange the sales data in ascending order: 600, 1100, 1200, 1600, 1700, 1700, 1800, 2000, 2200, 2300, 2400, 2900, 2900, 2900, 2900, 3700, 3900. There are n=17 data points. Step 2: Calculate the mean. The mean is the sum of all values divided by the number of values. Mean = ( x)/(n) = (600+1100+1200+1600+1700+1700+1800+2000+2200+2300+2400+2900+2900+2900+2900+3700+3900)/(17) Mean = (37600)/(17) ≈ 2211.76 The mean is \2211.76. Step 3: Calculate the median. Since there are 17 data points (an odd number), the median is the ((n+1)/2)-th value in the ordered list. Median position = (17+1)/(2) = 9-th value The 9th value in the ordered list is 2200. The median is \2200. Step 4: Calculate the mode. The mode is the value that appears most frequently in the dataset. The value 2900 appears 4 times, which is more than any other value. The mode is \2900. Step 5: Calculate the range. The range is the difference between the maximum and minimum values in the dataset. Range = Maximum Value - Minimum Value = \3900 - \600 = \3300 The range is \3300. Question #2) Calculate the mean, median, mode, range, variance, and standard deviation for the following dataset: 8; 2; 4; 0; 1; 3; 5; 10; 6; 11; 12; 3; 9; 7; 3; 8; 12; 14; 16; 18; 21 Step 1: Order the data. First, arrange the dataset in ascending order: 0, 1, 2, 3, 3, 3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 14, 16, 18, 21. There are n=21 data points. Step 2: Calculate the mean. The mean is the sum of all values divided by the number of values. Mean = ( x)/(n) = (0+1+2+3+3+3+4+5+6+7+8+8+9+10+11+12+12+14+16+18+21)/(21) Mean = (173)/(21) ≈ 8.24 The mean is 8.24. Step 3: Calculate the median. Since there are 21 data points (an odd number), the median is the ((n+1)/2)-th value in the ordered list. Median position = (21+1)/(2) = 11-th value The 11th value in the ordered list is 8. The median is 8. Step 4: Calculate the mode. The mode is the value that appears most frequently in the dataset. The value 3 appears 3 times, which is more than any other value. The mode is 3. Step 5: Calculate the range. The range is the difference between the maximum and minimum values in the dataset. Range = Maximum Value - Minimum Value = 21 - 0 = 21 The range is 21. Step 6: Calculate the variance. We will calculate the sample variance, s^2. s^2 = (x_i - x)^2n-1 Using the formula s^2 = ( x_i^2 - ( x_i)^2/n)/(n-1): x_i = 173 x_i^2 = 0^2+1^2+2^2+3^2+3^2+3^2+4^2+5^2+6^2+7^2+8^2+8^2+9^2+10^2+11^2+12^2+12^2+14^2+16^2+18^2+21^2 = 2108 s^2 = (2108 - (173)^2/21)/(21-1) = (2108 - 29929/21)/(20) s^2 = (2108 - 1425.190476)/(20) = (682.809524)/(20) ≈ 34.14 The variance is 34.14. Step 7: Calculate the standard deviation. The standard deviation is the square root of the variance. s = sqrt(s^2) = sqrt(34.1404762) ≈ 5.84 The standard deviation is 5.84. Question 3) Identify the outliers in the dataset below: 26-2037242899801202231 53416429 The provided data appears to be a string of numbers without clear delimiters to form a dataset. To identify outliers, a clear list of individual numerical values is required. Without a properly formatted dataset, it is not possible to perform the calculation. Question 4) Calculate the median, the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3), and identify all outliers in the dataset below. Please show the steps leading to your answers. 180250025540015691761631827166 171 The provided data appears to be a string of numbers without clear delimiters to form a dataset. To calculate quartiles and identify outliers, a clear list of individual numerical values is required. Without a properly formatted dataset, it is not possible to perform the calculation. Question 5) If Q1 = 5 and Q3 = 15, find the interquartile range and locate the lower and upper fences. Step 1: Find the Interquartile Range (IQR). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). IQR = Q3 - Q1 = 15 - 5 = 10 The interquartile range is 10. Step 2: Locate the lower fence. The lower fence is calculated as Q1 - 1.5 × IQR. Lower Fence = 5 - (1.5 × 10) = 5 - 15 = -10 The lower fence is -10. Step 3: Locate the upper fence. The upper fence is calculated as Q3 + 1.5 × IQR. Upper Fence = 15 + (1.5 × 10) = 15 + 15 = 30 The upper fence is 30$. Send me the next one 📸

Accepted Answer · 2026-06-23T19:49:54.340Z

Here are the calculations for your questions. Question #1) Calculate the mean, median, mode, and range for the following sales data: 1700; 2200; 2400; 2900; 1800; 3700; 1200; 2300; 600; 1600; 2000; 3900; 1100; 1700; 2900; 2900; 2900. Step 1: Order the data. First, arrange the sales data in ascending order: 600, 1100, 1200, 1600, 1700, 1700, 1800, 2000, 2200, 2300, 2400, 2900, 2900, 2900, 2900, 3700, 3900. There are n=17 data points. Step 2: Calculate the mean. The mean is the sum of all values divided by the number of values. Mean = ( x)/(n) = (600+1100+1200+1600+1700+1700+1800+2000+2200+2300+2400+2900+2900+2900+2900+3700+3900)/(17) Mean = (37600)/(17) ≈ 2211.76 The mean is \2211.76. Step 3: Calculate the median. Since there are 17 data points (an odd number), the median is the ((n+1)/2)-th value in the ordered list. Median position = (17+1)/(2) = 9-th value The 9th value in the ordered list is 2200. The median is \2200. Step 4: Calculate the mode. The mode is the value that appears most frequently in the dataset. The value 2900 appears 4 times, which is more than any other value. The mode is \2900. Step 5: Calculate the range. The range is the difference between the maximum and minimum values in the dataset. Range = Maximum Value - Minimum Value = \3900 - \600 = \3300 The range is \3300. Question #2) Calculate the mean, median, mode, range, variance, and standard deviation for the following dataset: 8; 2; 4; 0; 1; 3; 5; 10; 6; 11; 12; 3; 9; 7; 3; 8; 12; 14; 16; 18; 21 Step 1: Order the data. First, arrange the dataset in ascending order: 0, 1, 2, 3, 3, 3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 14, 16, 18, 21. There are n=21 data points. Step 2: Calculate the mean. The mean is the sum of all values divided by the number of values. Mean = ( x)/(n) = (0+1+2+3+3+3+4+5+6+7+8+8+9+10+11+12+12+14+16+18+21)/(21) Mean = (173)/(21) ≈ 8.24 The mean is 8.24. Step 3: Calculate the median. Since there are 21 data points (an odd number), the median is the ((n+1)/2)-th value in the ordered list. Median position = (21+1)/(2) = 11-th value The 11th value in the ordered list is 8. The median is 8. Step 4: Calculate the mode. The mode is the value that appears most frequently in the dataset. The value 3 appears 3 times, which is more than any other value. The mode is 3. Step 5: Calculate the range. The range is the difference between the maximum and minimum values in the dataset. Range = Maximum Value - Minimum Value = 21 - 0 = 21 The range is 21. Step 6: Calculate the variance. We will calculate the sample variance, s^2. s^2 = (x_i - x)^2n-1 Using the formula s^2 = ( x_i^2 - ( x_i)^2/n)/(n-1): x_i = 173 x_i^2 = 0^2+1^2+2^2+3^2+3^2+3^2+4^2+5^2+6^2+7^2+8^2+8^2+9^2+10^2+11^2+12^2+12^2+14^2+16^2+18^2+21^2 = 2108 s^2 = (2108 - (173)^2/21)/(21-1) = (2108 - 29929/21)/(20) s^2 = (2108 - 1425.190476)/(20) = (682.809524)/(20) ≈ 34.14 The variance is 34.14. Step 7: Calculate the standard deviation. The standard deviation is the square root of the variance. s = sqrt(s^2) = sqrt(34.1404762) ≈ 5.84 The standard deviation is 5.84. Question 3) Identify the outliers in the dataset below: 26-2037242899801202231 53416429 The provided data appears to be a string of numbers without clear delimiters to form a dataset. To identify outliers, a clear list of individual numerical values is required. Without a properly formatted dataset, it is not possible to perform the calculation. Question 4) Calculate the median, the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3), and identify all outliers in the dataset below. Please show the steps leading to your answers. 180250025540015691761631827166 171 The provided data appears to be a string of numbers without clear delimiters to form a dataset. To calculate quartiles and identify outliers, a clear list of individual numerical values is required. Without a properly formatted dataset, it is not possible to perform the calculation. Question 5) If Q1 = 5 and Q3 = 15, find the interquartile range and locate the lower and upper fences. Step 1: Find the Interquartile Range (IQR). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). IQR = Q3 - Q1 = 15 - 5 = 10 The interquartile range is 10. Step 2: Locate the lower fence. The lower fence is calculated as Q1 - 1.5 × IQR. Lower Fence = 5 - (1.5 × 10) = 5 - 15 = -10 The lower fence is -10. Step 3: Locate the upper fence. The upper fence is calculated as Q3 + 1.5 × IQR. Upper Fence = 15 + (1.5 × 10) = 15 + 15 = 30 The upper fence is 30$. Send me the next one 📸

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