the median of the following data: \( 50,60,70,80 \) and 90 . the value of \( x \) if its median is 70 . \[ 50,60, \frac{3 x+5}{2}, 80,90 \] the mean of the data:

To find the median of the given data set \( 50, 60, 70, 80, 90 \), we need to arrange the data in ascending order first: \( 50, 60, 70, 80, 90 \) The median is the middle value when the data set is arranged in ascending order. Since the data set has an odd number of values, the median is the middle value, which is 70. Given that the median is 70, we can find the value of \( x \) in the data set \( 50, 60, \frac{3x+5}{2}, 80, 90 \) by setting the median equal to 70 and solving for \( x \). The median is the middle value, so we have: \( \frac{3x+5}{2} = 70 \) Now, we can solve for \( x \) by multiplying both sides by 2 and then solving the resulting equation. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{3x+5}{2}=70\) - step1: Cross multiply: \(3x+5=2\times 70\) - step2: Simplify the equation: \(3x+5=140\) - step3: Move the constant to the right side: \(3x=140-5\) - step4: Subtract the numbers: \(3x=135\) - step5: Divide both sides: \(\frac{3x}{3}=\frac{135}{3}\) - step6: Divide the numbers: \(x=45\) The value of \( x \) is 45. Next, to find the mean of the data set \( 50, 60, \frac{3x+5}{2}, 80, 90 \), we need to calculate the sum of all the values and then divide by the total number of values. The sum of the data set is: \( 50 + 60 + \frac{3(45)+5}{2} + 80 + 90 \) Now, we can calculate the mean by dividing the sum by the total number of values. Calculate the value by following steps: - step0: Calculate: \(50+60+\frac{\left(3\times 45+5\right)}{2}+80+90\) - step1: Remove the parentheses: \(50+60+\frac{3\times 45+5}{2}+80+90\) - step2: Multiply the numbers: \(50+60+\frac{135+5}{2}+80+90\) - step3: Add the numbers: \(50+60+\frac{140}{2}+80+90\) - step4: Divide the terms: \(50+60+70+80+90\) - step5: Add the numbers: \(350\) The sum of the data set is 350. To find the mean, we divide the sum by the total number of values, which is 5 in this case. Mean = Sum of values / Total number of values Mean = 350 / 5 Mean = 70 Therefore, the mean of the data set \( 50, 60, \frac{3x+5}{2}, 80, 90 \) is 70.