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A set of data has the following values: 47, 34, 39, 25, 32, 17, 45, 50, 62, 64, 48, 54, 39, 22, 42, 17, 47, 34, 67. Calculate the median, range, mode, and mean.

Mathematics

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Answers

4 parts
a

42\text{42}

b

50\text{50}

c

17, 34, 39, 47\text{17, 34, 39, 47}

d

44.16\text{44.16}

Step-by-step solution

8 steps

Here are the answers to your questions.

Part 1

Part a

42\text{42}

Step 1: List the data in ascending order.

17,17,22,25,32,34,34,39,39,42,45,47,47,48,50,54,62,64,6717, 17, 22, 25, 32, 34, 34, 39, 39, 42, 45, 47, 47, 48, 50, 54, 62, 64, 67
  1. Determine the number of data points.

    There are n=19n = 19 data points.

  2. Calculate the position of the median.

    The median is the n+12\frac{n+1}{2}-th value.

    Position=19+12=202=10\text{Position} = \frac{19+1}{2} = \frac{20}{2} = 10
  3. Identify the median value.

    The 10th10^{th} value in the ordered list is 42.
    The median is 42\boxed{\text{42}}.

Part b

50\text{50}

Step 1: Identify the maximum and minimum values.

Maximum value = 67
Minimum value = 17

  1. Calculate the range.

    Range=Maximum value−Minimum value\text{Range} = \text{Maximum value} - \text{Minimum value} Range=67−17=50\text{Range} = 67 - 17 = 50

    The range is 50\boxed{\text{50}}, which confirms the statement that the range is 50%.

Part c

17, 34, 39, 47\text{17, 34, 39, 47}

Step 1: Count the frequency of each data point.

  • 17 appears 2 times
  • 22 appears 1 time
  • 25 appears 1 time
  • 32 appears 1 time
  • 34 appears 2 times
  • 39 appears 2 times
  • 42 appears 1 time
  • 45 appears 1 time
  • 47 appears 2 times
  • 48 appears 1 time
  • 50 appears 1 time
  • 54 appears 1 time
  • 62 appears 1 time
  • 64 appears 1 time
  • 67 appears 1 time
  1. Identify the value(s) with the highest frequency.

    The values 17, 34, 39, and 47 all appear 2 times, which is the highest frequency.
    The mode is 17, 34, 39, 47\boxed{\text{17, 34, 39, 47}}.

Part d

44.16\text{44.16}

Step 1: Sum all the data points.

Sum=45+17+34+48+47+42+39+22+54+17+32+67+25+39+34+64+47+50+62=839\text{Sum} = 45+17+34+48+47+42+39+22+54+17+32+67+25+39+34+64+47+50+62 = 839
  1. Divide the sum by the number of data points.

    Mean=SumNumber of data points=83919\text{Mean} = \frac{\text{Sum}}{\text{Number of data points}} = \frac{839}{19} Mean≈44.15789...\text{Mean} \approx 44.15789...
  2. Round the mean to two decimal places.

    The mean is 44.16\boxed{\text{44.16}}.

Part 2

Part 2.1· 1 step

Step 1: Locate Neuwied and Mainz on the map.

  1. Use the compass rose to determine the direction of Neuwied relative to Mainz.

    Neuwied is located to the *north

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