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Re-arrange the Sales data in ascending order. There 17 data Points, n=17. (i) Mean, (ii) Median, (iii) Mode

Mathematics

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You've done a good job starting the process, James, but there are a few corrections needed in your ordered list and the subsequent calculations. Let's go through it step by step.

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 2200,one2200, one 2300, one 2400,andfour2400, and four 2900s. Your ordered list had some values duplicated or missed. Here is the correct ordered list:
    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. Interpret the mode.

    The mode of $2900 indicates that $2900 is the most common sales value in this dataset.

  8. 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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