Question

Записаны измерения отрезков в сантиметрах: 33, 27, 32, 21, х. Найдите х, если известно, что медиана этого набора совпадает с его средним арифметическим.

Answer 1

Ответ: 33, 27 ,32 ,21, 15.
х=15

Answer 2

Problem Analysis

We are given a set of measurements in centimeters: 33, 27, 32, 21, and x. We need to find the value of x if the median of this set is equal to its arithmetic mean.

Solution

To find the value of x, we need to determine the median and arithmetic mean of the given set and set them equal to each other. Let's calculate the median and arithmetic mean step by step.

1. Median Calculation: - The median is the middle value of a set when it is arranged in ascending order. - Since we have five measurements, the middle value will be the third value when the set is arranged in ascending order. - Arranging the measurements in ascending order: 21, 27, 32, 33, x. - The median is the third value, which is 32.

2. Arithmetic Mean Calculation: - The arithmetic mean is the sum of all the values divided by the number of values. - The sum of the given measurements is 33 + 27 + 32 + 21 + x. - The number of measurements is 5. - The arithmetic mean is (33 + 27 + 32 + 21 + x) / 5.

Now, we can set the median equal to the arithmetic mean and solve for x.

Median = Arithmetic Mean: 32 = (33 + 27 + 32 + 21 + x) / 5

To solve for x, we can multiply both sides of the equation by 5 and then subtract the sum of the known values from both sides.

5 * 32 = 33 + 27 + 32 + 21 + x 160 = 113 + x

Finally, we can solve for x by subtracting 113 from both sides of the equation.

160 - 113 = x x = 47

Therefore, the value of x is 47.

Answer

The value of x is 47.