A set of particle sizes are measured in divisions: 4, 5, 6, 7, 8, 10, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24…

Question

A set of particle sizes are measured in divisions: 4, 5, 6, 7, 8, 10, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25. The calibration factor is double the square root of 16. a) Calculate the calibration f

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a) Step 1: Calculate the calibration factor. The calibration factor is double the square root of 16. Calibration factor = 2 × √(16) = 2 × 4 = 8 Step 2: Calculate the actual particle size for each number of divisions. The actual particle size is found by multiplying the number of divisions by the calibration factor (8). No of division — 4 — 5 — 6 — 7 — 8 — 10 — 12 — 14 — 16 — 17 — 18 — 19 — 20 — 22 — 23 — 24 — 25Actual particle size — 32 — 40 — 48 — 56 — 64 — 80 — 96 — 112 — 128 — 136 — 144 — 152 — 160 — 176 — 184 — 192 — 200 The calibration factor is 8. b) Step 1: Determine the mid-class (X) for each particle size range. For 0-50: X = (0+50)/(2) = 25; For 51-100: X = (51+100)/(2) = 75.5; For 101-150: X = (101+150)/(2) = 125.5; For 151-200: X = (151+200)/(2) = 175.5 Step 2: Determine the frequency (F) for each class by counting the actual particle sizes from part (a) that fall into each range. The actual particle sizes are: 32, 40, 48, 56, 64, 80, 96, 112, 128, 136, 144, 152, 160, 176, 184, 192, 200. 0-50: 32, 40, 48 ⇒ F = 3; 51-100: 56, 64, 80, 96 ⇒ F = 4; 101-150: 112, 128, 136, 144 ⇒ F = 4; 151-200: 152, 160, 176, 184, 192, 200 ⇒ F = 6 Step 3: Calculate Frequency × mid class (FX) for each class. Particle size — Mid class (X) — Frequency (F) — Frequency X mid class (FX)0-50 — 25 — 3 — 25 × 3 = 75; 51-100 — 75.5 — 4 — 75.5 × 4 = 302; 101-150 — 125.5 — 4 — 125.5 × 4 = 502; 151-200 — 175.5 — 6 — 175.5 × 6 = 1053 Step 4: Calculate the sum of frequencies (∑ F) and the sum of (FX) (∑ FX). ∑ F = 3 + 4 + 4 + 6 = 17; ∑ FX = 75 + 302 + 502 + 1053 = 1932 Step 5: Calculate the mean particle size using the formula (∑ FX)/(∑ F). Mean particle size = 1932/17 ≈ 113.65 The mean particle size is 113.65.

A set of particle sizes are measured in divisions: 4, 5, 6, 7, 8, 10, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25. The calibration factor is double the square root of 16. a) Calculate the calibration f

Answers

Step-by-step solution

Part a· 1 step

Calculate the actual particle size for each number of divisions.

Part b· 4 steps113.65

Determine the frequency (F) for each class by counting the actual particle sizes from part (a) that fall into each range.

Calculate Frequency $\times$ mid class (FX) for each class.

Calculate the sum of frequencies ( $\sum F$ ) and the sum of (FX) ( $\sum FX$ ).

Calculate the mean particle size using the formula $\frac{\sum FX}{\sum F}$ .

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A set of particle sizes are measured in divisions: 4, 5, 6, 7, 8, 10, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25. The calibration factor is double the square root of 16. a) Calculate the calibration f

Answers

Step-by-step solution

Part a· 1 step

Calculate the actual particle size for each number of divisions.

Part b· 4 steps113.65

Determine the frequency (F) for each class by counting the actual particle sizes from part (a) that fall into each range.

Calculate Frequency ×\times× mid class (FX) for each class.

Calculate the sum of frequencies (∑F\sum F∑F) and the sum of (FX) (∑FX\sum FX∑FX).

Calculate the mean particle size using the formula ∑FX∑F\frac{\sum FX}{\sum F}∑F∑FX​.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Calculate Frequency $\times$ mid class (FX) for each class.

Calculate the sum of frequencies ( $\sum F$ ) and the sum of (FX) ( $\sum FX$ ).

Calculate the mean particle size using the formula $\frac{\sum FX}{\sum F}$ .