Using a working mean of 42, find the average wage per worker. 2) Explain the coding formula method and use the above example with a working mean of 42 find the average wage.

Question 1

Answer · 2026-09-17T17:22:43.294Z

Here's how to solve both questions using the provided data and the coding formula method. I) Using a working mean of 42, find the average wage per worker. II) Explain the coding formula method and use the above example with a working mean of 42 to find the average wage. The coding formula method (also known as the assumed mean or step-deviation method) simplifies the calculation of the mean for grouped data. It involves choosing an assumed mean (A) and a class width (c) to transform the data into smaller, more manageable coded deviations (u_i). The formula for the mean (x) is: x = A + ( f_i u_i)/( f_i) × c Where: A is the assumed mean. f_i is the frequency of each class. u_i is the coded deviation, calculated as u_i = (x_i - A)/(c). x_i is the midpoint of each class interval. c is the class width. Let's apply this method to the given data with an assumed mean (A) of 42. Step 1: Calculate Midpoints (x_i) and Class Width (c) The class width c = 34 - 30 + 1 = 5. Wages — f_i — Midpoint (x_i)30-34 — 1 — 32 35-39 — 6 — 37 40-44 — 10 — 42 45-49 — 8 — 47 50-54 — 2 — 52 55-59 — 3 — 57 Step 2: Calculate Deviations (d_i = x_i - A) and Coded Deviations (u_i = (d_i)/(c)) We use A = 42 and c = 5. Wages — f_i — x_i — d_i = x_i - 42 — u_i = (d_i)/(5) — f_i u_i30-34 — 1 — 32 — 32 - 42 = -10 — (-10)/(5) = -2 — 1 × -2 = -2 35-39 — 6 — 37 — 37 - 42 = -5 — (-5)/(5) = -1 — 6 × -1 = -6 40-44 — 10 — 42 — 42 - 42 = 0 — (0)/(5) = 0 — 10 × 0 = 0 45-49 — 8 — 47 — 47 - 42 = 5 — (5)/(5) = 1 — 8 × 1 = 8 50-54 — 2 — 52 — 52 - 42 = 10 — (10)/(5) = 2 — 2 × 2 = 4 55-59 — 3 — 57 — 57 - 42 = 15 — (15)/(5) = 3 — 3 × 3 = 9 Step 3: Sum Frequencies and f_i u_i f_i = 1 + 6 + 10 + 8 + 2 + 3 = 30 f_i u_i = -2 - 6 + 0 + 8 + 4 + 9 = 13 Step 4: Calculate the Mean Wage Substitute the values into the coding formula: x = A + ( f_i u_i)/( f_i) × c x = 42 + (13)/(30) × 5 x = 42 + (65)/(30) x = 42 + (13)/(6) x = 42 + 2.1666... x ≈ 44.17 The average wage per worker is \44.17$

Question 2

Here's how to solve both questions using the provided data and the coding formula method. I) Using a working mean of 42, find the average wage per worker. II) Explain the coding formula method and use the above example with a working mean of 42 to find the average wage. The coding formula method (also known as the assumed mean or step-deviation method) simplifies the calculation of the mean for grouped data. It involves choosing an assumed mean (A) and a class width (c) to transform the data into smaller, more manageable coded deviations (u_i). The formula for the mean (x) is: x = A + ( f_i u_i)/( f_i) × c Where: A is the assumed mean. f_i is the frequency of each class. u_i is the coded deviation, calculated as u_i = (x_i - A)/(c). x_i is the midpoint of each class interval. c is the class width. Let's apply this method to the given data with an assumed mean (A) of 42. Step 1: Calculate Midpoints (x_i) and Class Width (c) The class width c = 34 - 30 + 1 = 5. Wages — f_i — Midpoint (x_i)30-34 — 1 — 32 35-39 — 6 — 37 40-44 — 10 — 42 45-49 — 8 — 47 50-54 — 2 — 52 55-59 — 3 — 57 Step 2: Calculate Deviations (d_i = x_i - A) and Coded Deviations (u_i = (d_i)/(c)) We use A = 42 and c = 5. Wages — f_i — x_i — d_i = x_i - 42 — u_i = (d_i)/(5) — f_i u_i30-34 — 1 — 32 — 32 - 42 = -10 — (-10)/(5) = -2 — 1 × -2 = -2 35-39 — 6 — 37 — 37 - 42 = -5 — (-5)/(5) = -1 — 6 × -1 = -6 40-44 — 10 — 42 — 42 - 42 = 0 — (0)/(5) = 0 — 10 × 0 = 0 45-49 — 8 — 47 — 47 - 42 = 5 — (5)/(5) = 1 — 8 × 1 = 8 50-54 — 2 — 52 — 52 - 42 = 10 — (10)/(5) = 2 — 2 × 2 = 4 55-59 — 3 — 57 — 57 - 42 = 15 — (15)/(5) = 3 — 3 × 3 = 9 Step 3: Sum Frequencies and f_i u_i f_i = 1 + 6 + 10 + 8 + 2 + 3 = 30 f_i u_i = -2 - 6 + 0 + 8 + 4 + 9 = 13 Step 4: Calculate the Mean Wage Substitute the values into the coding formula: x = A + ( f_i u_i)/( f_i) × c x = 42 + (13)/(30) × 5 x = 42 + (65)/(30) x = 42 + (13)/(6) x = 42 + 2.1666... x ≈ 44.17 The average wage per worker is \44.17$

Wages	$f_i$	$x_i$	$d_i = x_i - 42$	$u_i = \frac{d_i}{5}$	$f_i u_i$
30-34	1	32	$32 - 42 = -10$	$\frac{-10}{5} = -2$	$1 \times -2 = -2$
35-39	6	37	$37 - 42 = -5$	$\frac{-5}{5} = -1$	$6 \times -1 = -6$
40-44	10	42	$42 - 42 = 0$	$\frac{0}{5} = 0$	$10 \times 0 = 0$
45-49	8	47	$47 - 42 = 5$	$\frac{5}{5} = 1$	$8 \times 1 = 8$
50-54	2	52	$52 - 42 = 10$	$\frac{10}{5} = 2$	$2 \times 2 = 4$
55-59	3	57	$57 - 42 = 15$	$\frac{15}{5} = 3$	$3 \times 3 = 9$

Using a working mean of 42, find the average wage per worker. 2) Explain the coding formula method and use the above example with a working mean of 42 find the average wage.

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