Chapter 8, Problem 8.1CRE

a.

To determine

To find: histogram of the given data and also plot the relative frequencies and explain the distribution of weights of newborn babies.

Explanation of Solution

Given:

The dataset:

Weight(Grams)	Count
Less than 500	5980
500 - 999	22015
1000 - 1499	29846
1500 - 1999	63427
2000 - 2499	204295
2500 - 2999	744181
3000 - 3499	1566755
3500 - 3999	1055004
4000 - 4499	262997
4500 - 4999	36706
5000 - 5499	4216

Formula used:

  $\text{Relative}\text{Frequency = }\frac{\text{Frequency of class}}{\text{Total frequency}}$

Calculation:

Weight(Grams)	Relative frequency
Less than 500	0.001
500 - 999	0.006
1000 - 1499	0.007
1500 - 1999	0.016
2000 - 2499	0.051
2500 - 2999	0.186
3000 - 3499	0.392
3500 - 3999	0.264
4000 - 4499	0.066
4500 - 4999	0.009
5000 - 5499	0.001
Sum	1

Graph:

The histogram:

  

The relative frequency histogram:

  

Based on the above histogram, it looks that data is approximately normally distributed, though it has a bit larger tail towards the left side, so it can also be considered as the left skewed but since there is not so large difference in tails so it will be better to consider it as approximately normally distributed.

b.

To determine

To find the median class of the data.

Explanation of Solution

Formula used:

  $\text{Median = }{\left(\frac{N}{2}\right)}^{\text{Th term}}$

Calculation:

Weight(Grams)	Count	Cumulative frequency.
Less than 500	5980	5980
500 - 999	22015	27995
1000 - 1499	29846	57841
1500 - 1999	63427	121268
2000 - 2499	204295	325563
2500 - 2999	744181	1069744
3000 - 3499	1566755	2636499
3500 - 3999	1055004	3691503
4000 - 4499	262997	3954500
4500 - 4999	36706	3991206
5000 - 5499	4216	3995422
Sum	3995422

  $\text{Median = }\frac{\text{N}}{2}$

Median = $\frac{3995422}{2}=1997711$

Now, it required to see that in under which CF value does it falls.

The value 1997711 is less than 2636499, so the median value falls in the class 3000 − 3499.

c.

To determine

To construct the pie chart or bar chart to show the proportion of given categories.

Explanation of Solution

Given:

The categories:

Very low birth weight: Less than 1500 grams

Low birth weight: Less than 2500 grams

Normal birth weight: More than 2500 grams

Calculation:

Count of each category:

Category	Frequency	Proportion
Very low birth Weight	57841	0.0144768
Low birth weight	267722	0.0670072
Normal birth weight	3669859	0.918516

Graph:

  

d.

To determine

To explain the outcome of the analysis that is being done so far.

Explanation of Solution

Based on the graph prepared in the last part, it is clearly visible that about 8% child having risk of low weight at the time of birth, which indicates at huge proportion of total, it is not an unusual events of being a low weight baby at the time of birth. Tough the distribution if approximately normal but still a large proportion is under the risk of low weight.