Math Problem Statement

show me the calculations

Solution

Sure, let's go through the calculation for the median step by step.

Given marks: 66,68,70,82,78,67,79,81,75,9566, 68, 70, 82, 78, 67, 79, 81, 75, 95

  1. Arrange the marks in ascending order:

    66,67,68,70,75,78,79,81,82,9566, 67, 68, 70, 75, 78, 79, 81, 82, 95

  2. Determine the number of data points:

    There are 10 data points.

  3. Identify the median position:

    For an even number of data points, the median is the average of the two middle numbers. The middle numbers are the 5th and 6th values in the sorted list.

  4. Find the middle values:

    The 5th value is 75 and the 6th value is 78.

  5. Calculate the median:

    Median=75+782=1532=76.5\text{Median} = \frac{75 + 78}{2} = \frac{153}{2} = 76.5

So, the median of the given marks is 76.5.

Would you like any further details or have any other questions? Here are some possible follow-up questions:

  1. How do you calculate the mean of these marks?
  2. What is the mode of the given marks?
  3. Can you provide a box plot for this data set?
  4. How do you calculate the standard deviation of these marks?
  5. Can you show the range of the given marks?

Tip: When working with an even number of data points, always remember to average the two middle numbers to find the median.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Median

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12