Explain the coding formula method and use a mean of the above example to find the average wage per worker.

The coding formula method, also known as the assumed mean method or step-deviation method, simplifies the calculation of the mean, especially for grouped data or when data values are large. It involves shifting the origin and scaling the data to work with smaller, more manageable numbers. Step 1: Explain the Coding Formula Method The formula for the mean (x) using the coding method is: x = A + ( f_i u_i)/( f_i) × c Where: A is the assumed mean, a value chosen from the data (often the midpoint of a central class interval). f_i is the frequency of each class. u_i is the coded deviation for each class, calculated as u_i = (x_i - A)/(c). x_i is the midpoint of each class interval. c is the class width (or common factor) of the intervals. f_i u_i is the sum of the products of frequencies and coded deviations. f_i is the total frequency (total number of observations). Step 2: Create a Hypothetical Example Since the "above example" is not provided, let's create a hypothetical example for the wages of 40 workers to demonstrate the method. Assume the wages (in dollars) are grouped as follows: Wages () — Number of Workers (f_i)100-120 — 5 120-140 — 10 140-160 — 15 160-180 — 8 180-200 — 2 Total — f_i = 40 Step 3: Calculate Midpoints, Deviations, and Coded Deviations We choose an assumed mean (A) and class width (c). Let A = 150 (midpoint of the class with the highest frequency) and c = 20 (e.g., 120 - 100). Wages () — f_i — Midpoint (x_i) — d_i = x_i - A — u_i = (d_i)/(c) — f_i u_i100-120 — 5 — 110 — 110 - 150 = -40 — (-40)/(20) = -2 — 5 × -2 = -10 120-140 — 10 — 130 — 130 - 150 = -20 — (-20)/(20) = -1 — 10 × -1 = -10 140-160 — 15 — 150 — 150 - 150 = 0 — (0)/(20) = 0 — 15 × 0 = 0 160-180 — 8 — 170 — 170 - 150 = 20 — (20)/(20) = 1 — 8 × 1 = 8 180-200 — 2 — 190 — 190 - 150 = 40 — (40)/(20) = 2 — 2 × 2 = 4 Step 4: Sum the Frequencies and f_i u_i From the table: f_i = 40 f_i u_i = -10 - 10 + 0 + 8 + 4 = -8 Step 5: Calculate the Mean Wage Substitute the values into the coding formula: x = A + ( f_i u_i)/( f_i) × c x = 150 + (-8)/(40) × 20 x = 150 + (-0.2) × 20 x = 150 - 4 x = 146 The average wage per worker is \146$