Identify the given numbers and the mean.

Welcome back ~LIZZY💞🥺 — missed you this week. Here's how to solve the problem: Step 1: Identify the given numbers and the mean. The given numbers are 1, 4, k, 4 and k+1. There are n=5 numbers. The mean is given as k+1. Step 2: Use the formula for the mean to find k. The mean is the sum of all numbers divided by the count of numbers. Mean = ( x)/(n) Substitute the given values: k+1 = (1+4+k+4+(k+1))/(5) k+1 = (10+2k)/(5) Multiply both sides by 5: 5(k+1) = 10+2k 5k+5 = 10+2k Subtract 2k from both sides: 3k+5 = 10 Subtract 5 from both sides: 3k = 5 Divide by 3: k = (5)/(3) Step 3: Substitute the value of k back into the set of numbers and the mean. The numbers are 1, 4, k, 4, k+1. Substitute k = (5)/(3): 1, 4, (5)/(3), 4, (5)/(3)+1 1, 4, (5)/(3), 4, (8)/(3) The mean is k+1 = (5)/(3)+1 = (8)/(3). Step 4: Calculate the variance. The variance (^2) is the average of the squared differences from the mean. ^2 = (x_i - mean)^2n Calculate the differences from the mean: (1 - (8)/(3))^2 = ((3-8)/(3))^2 = (-(5)/(3))^2 = (25)/(9) (4 - (8)/(3))^2 = ((12-8)/(3))^2 = ((4)/(3))^2 = (16)/(9) ((5)/(3) - (8)/(3))^2 = (-(3)/(3))^2 = (-1)^2 = 1 = (9)/(9) (4 - (8)/(3))^2 = ((4)/(3))^2 = (16)/(9) ((8)/(3) - (8)/(3))^2 = (0)^2 = 0 Sum of squared differences: (x_i - mean)^2 = (25)/(9) + (16)/(9) + (9)/(9) + (16)/(9) + 0 = (25+16+9+16)/(9) = (66)/(9) Now calculate the variance: ^2 = (66)/(9)5 = (66)/(9 × 5) = (66)/(45) Simplify the fraction: ^2 = (22)/(15) Step 5: Calculate the standard deviation. The standard deviation () is the square root of the variance. = sqrt(^2) = sqrt((22)/(15)) ≈ sqrt(1.4667) ≈ 1.211 The value of k is (5)/(3) and the standard deviation is sqrt((22)/(15)) ≈ 1.211. Drop the next question.