Statistics Practice Question

Questions: The daily sales at a food store (sample) : $1,520, $2,620, $3,360, $3,550, $1,350, $2,545, $1,430, $2,400, $3,580, $2,390, $1,525, $2,400, $1,420, $1,550, $2,390, $1,560, $1,680, $2,330 1. Calculate the mean, median, mode, first quartile and third quartile. 2. Calculate the range, IQR, variance, standard deviation and Coefficient of variation. 3. What conclusion can you reach about the daily sales at this store? Answers: 1. The mean value of the daily sales at a food store is given by the average of all the values of daily sales at the food store. Mean = $ (1520+ 2620 + 3360 + 3550 + 1350 + 2545 + 1430 + 2400 + 3580 + 2390 + 1525 + 2400 + 1420 + 1550 + 2390 + 1560 + 1680 + 2330 ) / 18 = 39600 / 18 = 2200 On arranging the given values in ascending order, the daily sales at a food store are as follows: 1350, 1420, 1430, 1520, 1525, 1550, 1560, 1680, 2330, 2390, 2390, 2400, 2400, 2545, 2620, 3360, 3550, 3580. Median of the given data set is [(18/2)th observation + (18/2)th + 1 observation ] / 2 = {2330 + 2390} / 2 = 2360 Mode of the given sample is the value that occurs maximum number of times = 2400 and 2390. The lower half of the data set comprises of the data 1350, 1420, 1430, 1520, 1525, 1550, 1560, 1680, and 2330. Since, there are even numbers of numbers; Q1 denotes the median value of this lower half of the data set. Q1 = 1531.25 The upper half of the data set comprises of the data 2390, 2390, 2400, 2400, 2545, 2620, 3360, 3550 and 3580. Since, there are even numbers of numbers; Q3 denotes the median value of this upper half of the data set. Q3 = 2508.75 2. The minimum value of the data set is 1350 and the maximum value of the data set is 3580. The range of the values if given as maximum value minimum values = 3580 1350 = Inter Quartile Range = Q3 Q1 = 2508.75 1531.25 = 977.5. Variance is given by the formula (x mean)2 / (N-1) = 9481350 / 17 = 632090. Standard deviation of the data set is given by the formula sqrt ((x mean)2 / (N-1)) = sqrt (632090) = 746.8109. Coefficient of variation is given by the formula (standard deviation / mean) * 100 = (746.8109 / 2200) * 100 = 33.94595. 3. It is seen that the average value of the daily sales at a food store is given as $ 2200. The minimum value of sales that occurred in the store is $1350 and the maximum value of sales that occurred in the store is $3580. The range of the values of sales that occurred is $2230. The maximum values of the sales that took place is $2400. There was a high deviation in the value of daily sales as the standard deviation was found to be 8109.The coefficient of variation also had a high value of deviation and the value is 33.94595.