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Find (a) mean (b) median (c) modal from the distribution of numbers: 2, 3, 4, 5, 6, 7, 3, 2, 2, 1, 0, 8, 7, 1, 4, 3, 2, 6, 1, 2, 2, 0

Mathematics

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Answers

3 parts
a
3.17
b
2.5
c
2

Step-by-step solution

7 steps

Here are the calculations for the mean, median, and mode of the given distribution of numbers.

The numbers are: 2,3,4,5,6,7,3,2,3,2,2,1,0,8,7,1,4,3,2,6,1,2,2,02, 3, 4, 5, 6, 7, 3, 2, 3, 2, 2, 1, 0, 8, 7, 1, 4, 3, 2, 6, 1, 2, 2, 0.
There are n=24n = 24 numbers in total.

Part a· 2 steps

Mean

  1. Sum all the numbers.

    Sum=2+3+4+5+6+7+3+2+3+2+2+1+0+8+7+1+4+3+2+6+1+2+2+0=76\text{Sum} = 2+3+4+5+6+7+3+2+3+2+2+1+0+8+7+1+4+3+2+6+1+2+2+0 = 76

  2. Divide the sum by the total count of numbers (nn).

    Mean=Sumn=7624=196\text{Mean} = \frac{\text{Sum}}{n} = \frac{76}{24} = \frac{19}{6} Mean≈3.1666...\text{Mean} \approx 3.1666...

    The mean is 3.17\boxed{3.17} (rounded to two decimal places).

Part b2.5

Median

  1. Arrange the numbers in ascending order.

    0,0,1,1,1,2,2,2,2,2,2,2,3,3,3,3,4,4,5,6,6,7,7,80, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8

  2. Since there are n=24n=24 numbers (an even count), the median is the average of the two middle numbers.

    These are the numbers at the n2\frac{n}{2}-th and (n2+1)(\frac{n}{2} + 1)-th positions.
    The 12th number is 2.
    The 13th number is 3.

  3. Calculate the average of these two numbers.

    Median=2+32=52=2.5\text{Median} = \frac{2 + 3}{2} = \frac{5}{2} = 2.5

    The median is 2.5\boxed{2.5}.

Part c2

Mode

  1. Identify the frequency of each number in the sorted list.

    • 0 appears 2 times.
    • 1 appears 3 times.
    • 2 appears 7 times.
    • 3 appears 4 times.
    • 4 appears 2 times.
    • 5 appears 1 time.
    • 6 appears 2 times.
    • 7 appears 2 times.
    • 8 appears 1 time.

  2. The mode is the number that appears most frequently.

    The number 2 appears 7 times, which is more than any other number.
    The mode is 2\boxed{2}.

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