Question

crumbs cookies was interested in seeing if there was an association between cookie flavor and whether or not there was frosting. given are the results of the last weeks orders.
frosting no frosting total
sugar cookie 48
chocolate chip 60 136
red velvet 40
total 160 400
which category has the lowest joint frequency?
red velvet cookies
cookies with frosting
red velvet cookies with frosting
red velvet cookies without frosting

Explanation:

Step1: Fill Chocolate Chip Frosting

$136 - 60 = 76$

Step2: Fill Total No Frosting

$400 - 160 = 240$

Step3: Fill Red Velvet Total

$400 - (48+76+60+40) = 176$

Step4: Fill Red Velvet Frosting

$176 - 40 = 136$

Step5: Fill Sugar Cookie No Frosting

$240 - 60 - 40 = 140$

Step6: Fill Sugar Cookie Total

$48 + 140 = 188$

Step7: List all joint frequencies

Sugar Cookie Frosting: 48; Sugar Cookie No Frosting: 140; Chocolate Chip Frosting:76; Chocolate Chip No Frosting:60; Red Velvet Frosting:136; Red Velvet No Frosting:40

Step8: Identify lowest joint frequency

Compare all values: 40 is the smallest, which is Red Velvet No Frosting.

Answer:

Red velvet cookies without frosting