Calculate the mean and median for the given set of figures related to average pay.

Question

ScanSolve AI Tutor · Accepted Answer

Here is the completed table and the calculations: Completed Table: Average pay (x) — Tally — No. of people (f) — fx — x^2 — fx^218 — I — 1 — 18 — 324 — 324 21 — I — 1 — 21 — 441 — 441 22 — III — 3 — 66 — 484 — 1452 23 — II — 2 — 46 — 529 — 1058 25 — II — 2 — 50 — 625 — 1250 26 — I — 1 — 26 — 676 — 676 27 — I — 1 — 27 — 729 — 729 29 — II — 2 — 58 — 841 — 1682 ∑ f = 13 — ∑ fx = 312 — ∑ fx² = 7612 --- (a) Calculate, for this set of figures the: (i) Mean Step 1: Use the formula for the mean of grouped data. Mean (μ) = (∑ fx)/(∑ f) Step 2: Substitute the sums from the table. μ = 312/13 Step 3: Calculate the mean. μ = 24 The mean is 24 GHC. (ii) Median Step 1: Order the data points: 18, 21, 22, 22, 22, 23, 23, 25, 25, 26, 27, 29, 29 Step 2: Determine the position of the median. There are N=13 data points. Median position = (N+1)/(2)-th value = (13+1)/(2)-th value = 7-th value Step 3: Identify the 7th value in the ordered list. The 7th value is 23. The median is 23 GHC. (iii) Mode Step 1: Identify the value that appears most frequently in the data. From the frequency table, the value 22 appears 3 times, which is more than any other value. The mode is 22 GHC. (iv) Standard deviation Step 1: Use the formula for variance. Variance (σ²) = (∑ fx²)/(∑ f) − ((∑ fx)/(∑ f))² Step 2: Substitute the sums from the table. σ² = 7612/13 − (312/13)² Step 3: Calculate the terms. σ² = 585.5384615... − (24)²; σ² = 585.5384615... − 576; σ² = 9.5384615... Step 4: Calculate the standard deviation by taking the square root of the variance. Standard Deviation (σ) = √(σ²) = √(9.5384615...) σ ≈ 3.0884 The standard deviation is 3.09 GHC (rounded to two decimal places). --- (b) If all the data sets are decreased by GHC 2, what will the following become? (i) The new mean Step 1: When a constant is subtracted from every data point, the mean also decreases by that constant. New Mean = Original Mean − 2 Step 2: Substitute the original mean. New Mean = 24 − 2 = 22 The new mean is 22 GHC. (ii) The new standard deviation Step 1: Subtracting a constant from every data point shifts the entire distribution but does not change its spread or variability. Therefore, the standard deviation remains the same. New Standard Deviation = Original Standard Deviation Step 2: Substitute the original standard deviation. New Standard Deviation ≈ 3.09 The new standard deviation is 3.09 GHC.

Calculate the mean and median for the given set of figures related to average pay.

Answers

Step-by-step solution

Part a(i)· 3 steps

Use the formula for the mean of grouped data.

Substitute the sums from the table.