Transcript Tomatoes in a Bin

Tomatoes in a Bin
Consider a bin of tomatoes
that vary in weight with a
mean of 200 g and a
standard deviation of 24 g.
If we select a tomato at random from the bin, we will
be uncertain of its exact weight, but expect it to be in
the 200 g range.
If we chose two tomatoes, we might expect the weight
to be around 200  2 or 400g. Because the weights of
each tomato vary, we will expect some variability in
the weight of two tomatoes, of course.
Finding the mean for samples of two is obvious, but
finding the standard deviation is not.
If each tomato has variation in weight, then two tomatoes
will have more possible variation.
We don’t have a method of calculating the standard
deviation directly, and must apply the Rule for Variances.
Let X be the weight of the tomato.

2
X X
 
2
X
2
X
 2X  X  242  242

2
X X
 2(24 )  1152g
2
Recall that =24.
2
 X X  2 (24)  33.941g
Note that we did not multiply the standard deviation by 2.
Now suppose we select 5 tomatoes, again randomly. While
the mean weight is simply 5  200 =1000g, the standard
deviation is again more complicated.
 (X2  X X  X X)   2X   X2   2X   2X   2X  5 X2
2
2
2
 (X

5(24)

2880g
 X X  X X)
 (X  X X  X X)  5(24)  53.666g
Notice that we did not multiply by 5, but by the square
root of 5.
The following values are the weights of tomatoes in the
bin. Randomly select ten samples of two and calculate the
weight of each sample. Calculate the mean and standard
deviation of the sample weights.
Weights of tomatoes, in grams:
183
208
191
210
201
201
216
216
195
191
168
211
208
173
210
236
223
172
229
194
191
160
168
229
178
224
221
208
185
271
213
197
180
197
208
189
179
239
233
196
224
254
212
229
166
216
182
198
189
198
Now randomly select 10 samples of 5 tomatoes and record
the weight of each sample. Calculate the mean and standard
deviation and compare to our value calculated earlier.
Describe the method you used to make your random samples.
The end