Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc.,suspects irregularities in the payroll system,and orders an inspection of "each and every payroll voucher issued since January 1,1993." Each payroll voucher was inspected and the following frequency distribution was compiled. The median number of errors per voucher is __________.

Question

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc.,suspects irregularities in the payroll system,and orders an inspection of "each and every payroll voucher issued since January 1,1993." Each payroll voucher was inspected and the following frequency distribution was compiled.  The median number of errors per voucher is __________.

Quizplus · Accepted Answer

To find the median, we need to arrange the frequencies in ascending order from left to right until we reach the middle. The total number of vouchers is 1,200 (sum of frequencies). The middle term is the (1,200 + 1)/2 = 600. Starting from the left with a cumulative frequency of 0, we add the frequencies until we reach 600. The corresponding class interval is 1-2 errors with a frequency of 440. We can then use the formula: 
Median = L + [(n/2 - CF) / f] x W 
where L is the lower limit of the class interval, n is the total number of vouchers, CF is the cumulative frequency up to the previous class interval, f is the frequency of the median class interval, and W is the width of the class interval. 
Plugging in the values, we get: 
Median = 1 + [(600 - 220) / 440] x 1 
= 1 + (380/440) 
= 1 + 0.8636 
= 1.8636 
Rounding to the nearest whole number, the median number of errors per voucher is 3.