Question

An experiment was conducted to measure the effectiveness of various feedsupplements on the growth rate of chickens. A five number summary of theweights of the chicks in grams six weeks after hatching is as follows. Source:Anonymous (1948) Biometrika, 35, 214.• Min - 107• Q1 - 197• Median - 264• Q3 - 312• Max - 4261. Aboutpercent of the chicks weigh more than 1972. Aboutpercent of the chicks weigh more than 264.3. Aboutpercent of the chicks weigh more than 312.4. Aboutpercent of the chicks weigh between 197 and 312

Answer 1

We have a sample of x=weights with the following data:

• Min = 107

,

• Q1(x) = 197

,

• Median(x) = 264

,

• Q3(x) = 312

,

• Max(x) = 426

1) The percent of the chicks weight more than 197, this is the value of the Q1. The quartile 1 represent the value of x that the 25% of the sample has a value less o equal to that.

So the percent of chicks that have a weight greater than 197 is 75%.

2) For the weight more than 264, correspond to the Median, so the 50% of sample has a weight lower or equal 264, and the other 50% has a weight greater or equal to 264.

So, the percent is 50%.

3) The weight of 312 correspond with Q3, so the 75% of the sample has a weight less or equal to 312, and the other 35% has a weight greater than 312.

So, the percent is 25%.

4) The weigth are the percentil Q1 and Q3, respectively. So the percent of chicks that have a weigth between 197 and 312 is 75%-25% = 50%