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Calculate the Mean, Median, Mode, and range for the following Sales data.

Economics

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You've made good progress, James! You've correctly identified the number of data points and started the calculations. Let's refine your ordered list and then complete the calculations and interpretations.

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. Correct the ordered data.

    The original dataset has one 2200andfour2200 and four 2900s. Your ordered list had two 2200sandthree2200s and three 2900s. Let's correct it:
    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.

  2. Calculate the mean.

    First, let's sum the values from the correct ordered list:

    ∑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

    Now, calculate the mean:

    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 correct 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 9th value is 2200.Themedianis2200. The median is \boxed{\mathbf{$2200}}$.

  5. Interpret the median.

    The median of $2200 means that half of the sales values are below $2200 and half are above $2200. It is the middle value of the dataset when arranged in order.

  6. Calculate the mode.

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

  7. 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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