A double glazing firm compares the number of windows in customers' orders in one month and produces the following data [number of windows(frequency)]: 0 to 2(15); 3 to 5(6); 6 to 8(3). Calculate the standard deviation of this data (2 decimal places).
A) 7.10
B) 7.20
C) 7.30
D) 7.40

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we first need to find the mean (average) number of windows per order. We do this by finding the midpoint of each range, multiplying by the frequency, and then dividing by the total number of orders.Midpoints: (0+2)/2 = 1, (3+5)/2 = 4, (6+8)/2 = 7Multiplying by frequency: 1*15 = 15, 4*6 = 24, 7*3 = 21Total windows = 15 + 24 + 21 = 60Total orders = 15 + 6 + 3 = 24Mean = Total windows / Total orders = 60 / 24 = 2.5Next, we calculate the variance. We subtract the mean from each midpoint, square the result, multiply by the frequency, sum these values, and divide by the total number of orders.Variance calculation:[(1-2.5)^2 * 15] + [(4-2.5)^2 * 6] + [(7-2.5)^2 * 3] = 67.5Variance = 67.5 / 24 = 2.8125Standard deviation = sqrt(variance) = sqrt(2.8125) ≈ 1.68It seems there was a misunderstanding in the calculation or the options provided do not match the correct calculation based on the given data. The correct standard deviation based on the provided calculation steps should be approximately 1.68, which is not among the options. Therefore, a reevaluation of the data or the options might be necessary.

A Double Glazing Firm Compares the Number of Windows in Customers