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Дан ряд чисел: [tex]175, 172, 179, 171, 174, 170, 172, 169[/tex].

Найдите медиану и размах ряда.

Answer :

  • The median of the series is 172.
  • The range of the series is 10.

To find the median and range of the given set of numbers, we will follow these steps:

  1. List of Numbers: We start with the given list of numbers:

    [tex]175, 172, 179, 171, 174, 170, 172, 169[/tex]

  2. Sort the Numbers: We need to sort these numbers in ascending order:

    [tex]169, 170, 171, 172, 172, 174, 175, 179[/tex]

  3. Finding the Median:

    • The median is the middle value of a sorted dataset.
    • If the number of observations (n) is odd, the median is the middle number.
    • If the number of observations is even, the median is the average of the two middle numbers.

    In this case, there are 8 numbers (even), so we find the two middle numbers, which are the 4th and 5th numbers in the sorted list:

    • The 4th number is 172
    • The 5th number is also 172

    Now we calculate the median:

    [tex]\text{Median} = \frac{172 + 172}{2} = \frac{344}{2} = 172[/tex]

    So, the median is 172.

  4. Finding the Range:

    • The range is the difference between the highest and lowest values in the dataset.
    • The highest value (max) is 179 and the lowest value (min) is 169.

    Now we calculate the range:

    [tex]\text{Range} = \text{max} - \text{min} = 179 - 169 = 10[/tex]

    Hence, the range is 10.

The translation of the question is:

Given a series of numbers: [tex]175, 172, 179, 171, 174, 170, 172, 169[/tex].

Find the median and range of the series.

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Rewritten by : Barada

Sure! Let's find the median and the range of the given series of numbers: 175, 172, 179, 171, 174, 170, 172, 169.

Step 1: Sort the Numbers

First, we need to arrange the numbers in ascending order:

169, 170, 171, 172, 172, 174, 175, 179

Step 2: Find the Median

The median is the middle number in a sorted list. If the list has an even number of elements, the median is the average of the two middle numbers.

- Our sorted list has 8 numbers, which is an even number.
- The two middle numbers are 172 and 172 (4th and 5th numbers).

To find the median, calculate the average of these two middle numbers:

[tex]\[
\text{Median} = \frac{172 + 172}{2} = \frac{344}{2} = 172.0
\][/tex]

The median of the series is 172.0.

Step 3: Calculate the Range

The range is the difference between the largest and the smallest numbers in the series.

- The smallest number is 169.
- The largest number is 179.

Now, subtract the smallest number from the largest number to find the range:

[tex]\[
\text{Range} = 179 - 169 = 10
\][/tex]

The range of the series is 10.

So, the median is 172.0 and the range is 10.