. Determine the median from the following data: X f 10 2 12 5 14 16 18 20 22 12 20 10 7 3

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Step 1: Calculate the total number of observations (N) The total frequency is the sum of all frequencies. N = 2 + 5 + 16 + 20 + 12 + 10 + 7 + 3 = 75 Step 2: Determine the position of the median The median position for an odd number of observations is given by (N+1)/(2). Median Position = (75+1)/(2) = 76/2 = 38th observation Step 3: Create a cumulative frequency distribution We need to find which value corresponds to the 38th observation. X (Value) — f (Frequency) — Cumulative Frequency (cf)10 — 2 — 2 12 — 5 — 2 + 5 = 7; 14 — 16 — 7 + 16 = 23; 16 — 20 — 23 + 20 = 43; 18 — 12 — 43 + 12 = 55; 20 — 10 — 55 + 10 = 65; 22 — 7 — 65 + 7 = 72; 24 — 3 — 72 + 3 = 75 Step 4: Identify the median value The 38th observation falls within the cumulative frequency range of 43. This corresponds to the X value of 16. The median is 16.

. Determine the median from the following data: X f 10 2 12 5 14 16 18 20 22 12 20 10 7 3

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Step-by-step solution

Calculate the total number of observations (N)

Determine the position of the median

Create a cumulative frequency distribution

Identify the median value

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