Question

an experiment was conducted to measure the effectiveness of various feed supplements on the growth rate of chickens. a five - number summary of the weights of the chicks in grams six weeks after hatching is as follows. source: anonymous (1948) biometrika, 35, 214.

• min = 107
• q1 = 198
• median = 246
• q3 = 328
• max = 418

1. about percent of the chicks weigh more than 198.
2. about percent of the chicks weigh more than 246.
3. about percent of the chicks weigh more than 328.
4. about percent of the chicks weigh between 198 and 328.

Explanation:

Step1: Recall quartile properties

In a five - number summary, Q1 is the first quartile (25th percentile), the median is the second quartile (50th percentile), and Q3 is the third quartile (75th percentile).

Step2: Solve for the percentage of chicks weighing more than 198

Since Q1 = 198, and Q1 represents the 25th percentile, the percentage of data above Q1 is \(100 - 25=75\).

Step3: Solve for the percentage of chicks weighing more than 246

Since the median = 246, and the median represents the 50th percentile, the percentage of data above the median is \(100 - 50 = 50\).

Step4: Solve for the percentage of chicks weighing more than 328

Since Q3 = 328, and Q3 represents the 75th percentile, the percentage of data above Q3 is \(100 - 75=25\).

Step5: Solve for the percentage of chicks weighing between 198 and 328

The percentage of data between Q1 and Q3 is \(75 - 25 = 50\).

Answer:

1. 75
2. 50
3. 25
4. 50