This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Sort the data set. The data set from the previous question, representing the amount of time spent (in minutes) by 32 customers, is: 18, 25, 30, 15, 12, 28, 35, 22, 10, 40, 17, 20, 23, 32, 27, 19 21, 26, 31, 16, 13, 29, 36, 24, 11, 41, 18, 21, 24, 33, 28, 20 Sorted data (n=32): 10, 11, 12, 13, 15, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 35, 36, 40, 41 Step 2: Calculate the percentage of quick shoppers (1.2.3). Quick shoppers are customers who spent 20 minutes or less. From the sorted data, the values 20 are: 10, 11, 12, 13, 15, 16, 17, 18, 18, 19, 20, 20. There are 12 quick shoppers. Total number of customers = 32. Percentage of quick shoppers = Number of quick shoppersTotal customers × 100\% Percentage of quick shoppers = (12)/(32) × 100\% Percentage of quick shoppers = 0.375 × 100\% Percentage of quick shoppers = 37.5\% Step 3: Identify an outlier in the data set (1.2.4). To identify an outlier, we can use the 2-standard deviation rule. First, calculate the mean (x) and standard deviation (). Sum of all values ( x) = 752 Number of values (n) = 32 x = ( x)/(n) = (752)/(32) = 23.5 The sum of squared differences from the mean ( (x_i - x)^2) = 2218 (calculated in thought process). = sqrt( (x_i - x))^2n-1 = sqrt((2218)/(31)) ≈ sqrt(71.548) ≈ 8.458 Outliers are typically values that fall outside the range of x ± 2. Lower bound = 23.5 - 2(8.458) = 23.5 - 16.916 = 6.584 Upper bound = 23.5 + 2(8.458) = 23.5 + 16.916 = 40.416 Any value less than 6.584 or greater than 40.416 is considered an outlier. Looking at the sorted data, the value 41 is greater than 40.416. The outlier is 41. Step 4: Match the definitions with the terminology (1.3). Using TABLE 2: TERMINOLOGY USED IN MATHEMATICAL LITERACY. 1.3.1 Mode: Value or values appearing most often in a data set. This matches definition G*. 1.3.2 50%: The even chance probability. This matches definition F*. 1.3.3 Median: Middle value in an ordered data set. This matches definition A*. 1.3.4 Mean: Sum of all values divided by the number of values. This matches definition B*. 1.3.5 IQR (Interquartile Range): The spread of the middle 50% of the data. This matches definition C*. 1.3.6 Breakeven point: The income received from the item sold and the cost price of the item are the same. This matches definition E*. The matches are: 1.3.1 G 1.3.2 F 1.3.3 A 1.3.4 B 1.3.5 C 1.3.6 E That's 2 down. 3 left today — send the next one.