A set of data that shows temperature highs for 10 days and satisfies all conditions below mean:72 median:74 mode:68 range:21

Question

A set of data that shows temperature highs for 10 days and satisfies all conditions below mean:72 median:74 mode:68 range:21

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Thanh Hà 1 week 2021-07-22T11:40:18+00:00 1 Answers 4 views 0

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    2021-07-22T11:41:57+00:00

    Answer:

    58, 68, 68, 68, 74, 74, 76, 77, 78, 79

    Step-by-step explanation:

    Given

    n=10

    Mean = 72

    Median = 74

    Mode = 68

    Range = 21

    Required

    The complete dataset

    The question has missing options (available online)

    From the mean, we have:

    Mean = \frac{\sum x}{n}

    This gives:

    72 = \frac{\sum x}{10}

    Cross  multiply

    \sum x = 72 * 10

    \sum x = 720

    This means that the sum of all elements of the dataset is 720

    Next, we test the median

    Since n = 10, then:

    Median = \frac{n + 1}{2}

    Median = \frac{10 + 1}{2}

    Median = \frac{11}{2}

    Median = 5.5th

    This implies that the median is the average of the 5th and 6th item.

    So, we have:

    Median = \frac{5th + 6th}{2}

    Cross multiply

    5th + 6th = 2 * Median

    5th + 6th = 2 * 74

    5th + 6th = 148

    This means that the 5th and 6th element add up to 148

    Also, we have:

    Mode = 68

    This means that 68 has to appear at least twice in the dataset

    Range = 21

    This implies that the difference between the highest and the least is 21.

    The dataset that satisfies the above condition is:


    58, 68, 68, 68, 74, 74, 76, 77, 78, 79

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