Question

With the rise in fuel costs, the price unit cost of the majority of beef products have increased, you are interested in the cost of 700kg fillet. The price of a 700g fillet steak in dollars was taken from the menus of 30 restaurants. The prices are as follows:

148 , 95 , 150 , 125 , 75 , 185 , 105 , 165 , 139 , 185

205 , 126 , 144 , 95 , 151 , 310 ,110 , 99 , 180 , 146

70 , 148, 160 , 138 , 89 , 146 , 180 , 170 , 123 , 170

a. Calculate and interpret the mean, median and modal price of 700 fillet steak meal from the 30 menus of the samples restaurants.

b. Calculate the standard deviation, coefficient of variation,

c. Calculate the quartile deviation of prices

Answer 1

( a )

Mean = Sum of terms / Number of terms

         = 4332 / 30

         = 144.4

• the mean price of 700 fillet steak meal from the 30 menus of the samples restaurants is 144.4

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

70   75   89   95   95   99   105   110   123   125   126   138   139   144   146   146   148   148   150   151   160   165   170   170   180   180   185   185   205   310   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = ( 146+146) / 2 = 146

• the median price of 700 fillet steak meal from the 30 menus of the samples restaurants is 146

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

70   75   89   95   95   99   105   110   123   125   126   138   139   144   146   146   148   148   150   151   160   165   170   170   180   180   185   185   205   310   

Since 6 values occurs 2 times, there is no mode for this data set.

• No mode for the price of 700 fillet steak meal from the 30 menus of the samples restaurants

( b )

Sample Standard deviation

( c )