3. Measures of location Percentiles and quartiles Aa Aa A growth chart is a plot

Question

3. Measures of location Percentiles and quartiles Aa Aa A growth chart is a plot of the percentiles of growth measurements, such as weight and height, for a population of infants or children. It is used by pediatricians to assess a child's growth over time The Centers for Disease Control and Prevention (CDC) is a U.S. agency devoted to the protection and promotion of public health. Through one of its units, the National Center for Health Statistics (NCHS), the CDC has developed growth charts for clinical use by health professionals. The most recent charts were published in 2000 The 2000 CDC growth charts were developed using a reference population of infants. A pediatrician looks up one of the charts and finds that the 97th percentile for weights of baby girls at 8-1/2 months is 24.8 pounds. This means that of the 8-1/2-month-old baby girls in the reference population weigh 24.8 pounds or less, and of these baby girls weigh 24.8 pounds or more. The 2000 CDC growth charts use a reference population of both breast-fed and formula-fed infants. It has been observed that breast-fed babies tend to gain weight more rapidly than formula-fed babies in the first 2 to 3 months of their lives, but they tend to weigh less than formula-fed babies from 6 to 12 months Sarah is a healthy baby who was exclusively breast-fed for her first 12 months. Which of the following is most likely a description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population? O 40th percentile at 3 months; 40th percentile at 6 months; 40th percentile at 9 months; 40th percentile at 12 months O 80th percentile at 3 months; 80th percentile at 6 months; 80th percentile at 9 months; 90th percentile at 12 months O 70th percentile at 3 months; 40th percentile at 6 months; 30th percentile at 9 months; 25th percentile at 12 months 20th percentile at 3 months; 50th percentile at 6 months; 80th percentile at 9 months; 90th percentile at 12 months The following are weights (in pounds) for a sample of 11 baby girls at the age of 10 months: 17.2 18.4 18.8 20.3 20.6 21.1 22 23.5 24.6 25,4 26.8 The 80th percentile for these sample data is pounds. In the sample data, observations are greater than or equal to this value out of 11 observations are less than or equal to the 80th percentile, and out of 11 For any data set, the first quartile is the percentile, the second quartile is the percentile percentile and the , and the third quartile is the In the prior sample data, the first quartile is interquartile range is pounds, and the third quartile is Therefore, the

Explanation / Answer

97th percentile means 97% of 8-1/2-month-old baby girls weigh 24.8 pounds or less, and 3% of these baby girls weigh 24.8 pounds or more.

In the first 2-3 months, breast fed babies gain weight more rapidly than formula fed babies but tend to weigh less than formula-fed babies from 6 to 12 months. This means, if we take data and observe the percentile of weight of a breast fed baby at different times, initially the percentile would be higher as she weighs more but the percentile reduces gradually as we consider the data at higher months. Thus, 3rd option is most likely a description of her weights. That is, 70th percentile at 3 months, 40th percentile at 6 months, 30th percentile at 9 months, and 25th percentile at 12 months. And here from 3rd month to 6th month the percentile reduced from 70th to 40th because till 3rd month, the baby tend to gain weight more rapidly and from 6th month, tend to weigh less and so, from 6th month to 9th and further to 12th month, the reduction in percentile is not as high as it is from 3rd to 6th, this clearly makes the 3rd option most likely for the given information in the question. It is assumed that the weights are sorted in an ascending order before determining the percentiles.

The given weights for a sample of 11 baby girls are in ascending order:

n =11, we need to get 80th percentile. 80%=0.80

0.80*11 = 8.8

The nearest whole number to 8.8 is 9 and in the given data, the 9th value(count from left to right) is 24.6

Thus, the 80th percentile for these sample data is 24.6 pounds.

For any data, the first quartile is the 25th percentile, the second quartile is the 50th percentile and the third quartile is the 75th percentile.

First quartile, Q1 = [(1/4)(n+1)]th term = [(1/4)(12)]th term = 3rd term = 18.8 pounds.

Third quartile, Q3 = [(3/4)(n+1)]th term = (3/4)(12)the term = 9th term = 24.6 pounds.

Inter quartile range = IQR = Q3 - Q1 = 24.6 - 18.8 = 5.8

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