Measurement #1 - Questions and Answers

Question 1 Determine the level of measurement of the variable. Favorite color Choose the correct level of measurement. A) Interval B) Nominal C) Ratio D) Ordinal Answer 1 Step 1 The variable "favorite color" is measured at the nominal level of measurement, that is, option (B). The nominal level of measurement is the level of data measurement where numbers are only used to categorize the data and have no quantitative significance. The words, letters and the alpha-numeric symbols can also be used in this level of measurement. Step 2 The option, "Ordinal" can be correct because the favorite color does not have a defined order. Similarly, the variable "favorite color" does not meet the requirements of ratio and interval level of measurement. Step 3 Thus, option (B), "Nominal" is the correct level of measurement. Question 2 8 gallons equals how many pints? Answer 8   gallons = 8 × 8   pints = 64   pints 8gallons=8×8pints=64pints Question 3 An airplane needs to reach a velocity of 203.0 km/h to take off. On a 2000 m runway, what is the minimum acceleration necessary for the plane to take flight? a) 0.79 m/s² b) 1.10 m/s² c) 0.95 m/s² d) 0.87 m/s² Answer 1 We can solve using the equation: 𝑣 2 = 𝑢 2 + 2 𝑎 𝑠 v 2 =u 2 +2as where 𝑠 s is the distance over which the acceleration occurs. Solving this for 𝑎 a, we have: 𝑎 = 𝑣 2 − 𝑢 2 2 𝑠 a= 2s v 2 −u 2 ​ We need to convert our velocity to units of m/s, so first multiply by 1000 m/km and divide by 3600 s/h, which gives: 𝑣 𝑓 = ( 203   km/h ) × 1000   m 3600   s = 56.4   m/s v f ​ =(203km/h)× 3600s 1000m ​ =56.4m/s Now, we just insert 𝑣 𝑓 = 56.4   m/s ,   𝑣 0 = 0 v f ​ =56.4m/s,v 0 ​ =0, and 𝑠 = 2000   m s=2000m into our equation, giving: 𝑎 = ( 56.4 ) 2 2 ( 2000 ) = 0.79   m/s 2 a= 2(2000) (56.4) 2 ​ =0.79m/s 2 So our answer is a) 0.79 m/s². Question 4 How much is 168 cm in inches? And in feet? Answer 1 One inch is 2.54 centimeters, so: Each cm is equal to:  1 2.54 = 0.3937 Each cm is equal to:  2.54 1 ​ =0.3937 Thus, we have: 168   cm × 0.3937 = 66.1416   inches. 168cm×0.3937=66.1416inches. Twelve inches make up each foot, making 60 inches equal to five feet. 168 cm are approximately  5   feet and  6   inches. 168 cm are approximately 5feet and 6inches. Question 5 Standard deviation is an indication of the... a. precision of one measurement b. accuracy of one measurement c. precision of repeated measurements Answer Step 1 Standard deviation: A number which is used to inform how measurements for a group are spread out from the mean value is called standard deviation. If most of the numbers are close to the mean value, the standard deviation will be low and if the numbers are more spread out, standard deviation will be high. Precision: Precision means how close is the value from the previously measured value of any measurement. Precision does not refer to the true value. Accuracy: The measured value which is close to the exact value is called accuracy. Step 2 From the above definitions, it is evident that standard deviation is the deviation of a group of measurements from their mean value and also the precision tells how close a particular measurement is from its mean measurement value. Since mean cannot be determined for any given single measurement, so precision cannot be determined for a single measurement. Therefore, option (a) is incorrect. Step 3 Since standard deviation tells the deviation from mean value but the accuracy tells how close to the exact value of any measurement. Hence, option (b) is also incorrect. Result: Hence, standard deviation is an indication of the precision of repeated measurements. So option (c) is correct.