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 = 105
Q1 = 196
Median = 263
Q3 = 317
Max = 413
1.About____percent of the chicks weigh more than 196.
2.About____percent of the chicks weigh more than 263.
3.About____percent of the chicks weigh more than 317.
4.About_____percent of the chicks weigh between 196 and 317.
196=Q1, so 1/4 weigh less than 196. So, 3/4 = 75% weigh more than 196
and so on for the rest
1. About 50 percent of the chicks weigh more than 196. Don't worry, they're not heavy... they're just well fed!
2. About 50 percent of the chicks weigh more than 263. Looks like these chickens are really putting on some weight! They must be eating their greens!
3. About 25 percent of the chicks weigh more than 317. These chickens are reaching for the stars with their weight! They must be channeling their inner bodybuilders.
4. About 50 percent of the chicks weigh between 196 and 317. We've got some good middle-of-the-road chickens here! They're not too light, and they're not too heavy. Just the right balance!
1. To find the percentage of chicks that weigh more than 196, we need to calculate the interquartile range (IQR) first. IQR = Q3 - Q1. Thus, IQR = 317 - 196 = 121. Since Q1 represents the 25th percentile and 196 falls within this range, we know that 25% of the chicks weigh less than or equal to 196. Therefore, 100% - 25% = 75% of the chicks weigh more than 196.
2. To find the percentage of chicks that weigh more than 263, we use the same logic as above. Since the median (263) represents the 50th percentile, we know that 50% of the chicks weigh less than or equal to 263. Therefore, 100% - 50% = 50% of the chicks weigh more than 263.
3. Using the same approach, since Q3 represents the 75th percentile and 317 falls within this range, we know that 75% of the chicks weigh less than or equal to 317. Therefore, 100% - 75% = 25% of the chicks weigh more than 317.
4. To find the percentage of chicks that weigh between 196 and 317, we can subtract the percentage of chicks that weigh less than or equal to 196 from the percentage of chicks that weigh less than or equal to 317. Since 25% of the chicks weigh more than 196 and 75% of the chicks weigh less than or equal to 317, the percentage of chicks that weigh between 196 and 317 is 75% - 25% = 50%.
To answer these questions, we can use the given five-number summary of the weights of the chicks. The five-number summary consists of the minimum (Min), the first quartile (Q1), the median, the third quartile (Q3), and the maximum (Max).
1. To find the percentage of chicks weighing more than 196 grams, we need to determine the proportion of chicks between Q1 and the maximum value (Max). Since we know the value of Q1 and Max, we can calculate the range between them:
Range = Max - Q1 = 413 - 196 = 217
The percentage of chicks weighing more than 196 grams can be calculated by dividing the range by the total range of the data and multiplying by 100:
Percentage of chicks weighing more than 196 = (Range / Total Range) * 100
Total Range = Max - Min = 413 - 105 = 308
Percentage of chicks weighing more than 196 = (217 / 308) * 100 ≈ 70.45%
Therefore, about 70.45% of the chicks weigh more than 196 grams.
2. Similarly, to find the percentage of chicks weighing more than 263 grams, we need to calculate the range between the median and the maximum:
Range = Max - Median = 413 - 263 = 150
Percentage of chicks weighing more than 263 = (Range / Total Range) * 100 = (150 / 308) * 100 ≈ 48.70%
Therefore, about 48.70% of the chicks weigh more than 263 grams.
3. To find the percentage of chicks weighing more than 317 grams, we calculate the range between Q3 and the maximum:
Range = Max - Q3 = 413 - 317 = 96
Percentage of chicks weighing more than 317 = (Range / Total Range) * 100 = (96 / 308) * 100 ≈ 31.17%
So, approximately 31.17% of the chicks weigh more than 317 grams.
4. To find the percentage of chicks weighing between 196 and 317 grams, we need to subtract the percentage of chicks weighing more than 317 from the percentage of chicks weighing more than 196:
Percentage of chicks weighing between 196 and 317 = Percentage of chicks weighing more than 196 - Percentage of chicks weighing more than 317 ≈ 70.45% - 31.17% ≈ 39.28%
Hence, approximately 39.28% of the chicks weigh between 196 and 317 grams.