Question : Find the standard deviation of the following data (rounded off to two decimal places). 5, 3, 4, 7
Option 1: 1.48
Option 2: 3.21
Option 3: 4.12
Option 4: 2.45
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Correct Answer: 1.48
Solution : Standard deviation of 5, 3, 4, 7 = $\sqrt{\frac{\sum {x_i}^2}{n}-(\frac{\sum x_i}{n})^2}$ where $x_i$ are the numbers and $n$ is the count of numbers. = $\sqrt{\frac{5^2+3^2+4^2+7^2}{4}-(\frac{5+3+4+7)}{4})^2}$ = $\sqrt{\frac{99}{4}-\frac{361}{16}}$ = $\sqrt{\frac{35}{16}}$ = 1.48 Hence, the correct answer is 1.48.
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Question : If the diameter of a sphere is 7 cm, find the volume of the sphere. (use $\pi=\frac{22}{7}$) (Rounded up to two decimal places).
Option 1: $184 \ \text{cm}^3$
Option 2: $201.34\ \text{cm}^3$
Option 3: $128.87 \ \text{cm}^3$
Option 4: $179.67 \ \text{cm}^3$
Question : The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:
Option 1: 4
Option 2: 5
Option 3: 14
Option 4: 20
Question : What is the mode of the given data? 5, 7, 9, 7, 3, 7, 5, 7, 8, 6, 7
Option 1: 7
Option 2: 6
Option 3: 5
Option 4: 3
Question : The hour hand moves through 4 hours and has a length of 6 cm. Find the area (in cm2, rounded off to two decimal places) of the sector covered by the hour hand.
Option 1: 32.69
Option 2: 30.67
Option 3: 37.71
Option 4: 35.75
Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary. 1. Fustian 2. Funerary 3. Fusion 4. Funicular 5. Fuscous 6. Fundament 7. Fuselage
Option 1: 6, 2, 5, 7, 3, 4, 1
Option 2: 6, 2, 5, 7, 4, 1, 3
Option 3: 6, 2, 4, 5, 7, 3, 1
Option 4: 6, 2, 5, 4, 7, 3, 1
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