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Calculate the mean, median, mode and range for the following Sales data: 1,700, 2,200, 2,400, 2,900, 1,800, 3,700, 1,200, 2,300, 600, 1,600, 2,000, 3,900, 1,100, 1,700, 2,900, 2,900, $2,900. Then, interpret the result.

Mathematics

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You've done a great job re-arranging the data and setting up the mean calculation. Let's refine the sum and complete the rest of the question.

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.

  1. Use the ordered data and correct the sum.

    You correctly re-arranged the sales data in ascending order:
    600,600, 1100, 1200,1200, 1600, 1700,1700, 1700, 1800,1800, 2000, 2200,2200, 2300, 2400,2400, 2900, 2900,2900, 2900, 2900,2900, 3700, 3900.Thereare3900. There are n=17$ data points.
    Let's re-sum the values:

    ∑x=600+1100+1200+1600+1700+1700+1800+2000+2200+2300+2400+2900+2900+2900+2900+3700+3900=37600\sum x = 600+1100+1200+1600+1700+1700+1800+2000+2200+2300+2400+2900+2900+2900+2900+3700+3900 = 37600

    Your sum of 37,100wasslightlyoff.Thecorrectsumis37,100 was slightly off. The correct sum is 37,600.

  2. Calculate the mean.

    The mean is the sum of all values divided by the number of values.

    Mean=∑xn=3760017≈2211.7647\text{Mean} = \frac{\sum x}{n} = \frac{37600}{17} \approx 2211.7647

    Rounding to two decimal places:
    The mean is \boxed{\mathbf{\2211.76}}$.

  3. Interpret the mean.

    The mean of 2211.76indicatesthatthe∗average∗salesvalueacrossall17datapointsisapproximately2211.76 indicates that the *average* sales value across all 17 data points is approximately 2211.76. It represents the central tendency of the sales data.

  4. Calculate the median.

    Since there are 17 data points (an odd number), the median is the ((n+1)/2)((n+1)/2)-th value in the ordered list.

    Median position=17+12=9-th value\text{Median position} = \frac{17+1}{2} = 9\text{-th value}

    Counting to the 9th value in the ordered list:
    600,1100,1200,1600,1700,1700,1800,2000,2200,2300,2400,2900,2900,2900,2900,3700,3900600, 1100, 1200, 1600, 1700, 1700, 1800, 2000, \mathbf{2200}, 2300, 2400, 2900, 2900, 2900, 2900, 3700, 3900.
    The median is \boxed{\mathbf{\2200}}$.

  5. Calculate the mode.

    The mode is the value that appears most frequently in the dataset.
    The value 2900appears4times,whichismorethananyothervalue.Themodeis2900 appears 4 times, which is more than any other value. The mode is \boxed{\mathbf{$2900}}$.

  6. Calculate the range.

    The range is the difference between the maximum and minimum values in the dataset. Range=Maximum Value−Minimum Value=$3900−$600=$3300\text{Range} = \text{Maximum Value} - \text{Minimum Value} = \$3900 - \$600 = \$3300 The range is \boxed{\mathbf{\3300}}$.

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