a.
To find: histogram of the given data and also plot the relative frequencies and explain the distribution of weights of newborn babies.
a.
![Check Mark](/static/check-mark.png)
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:
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
b.
To find the median class of the data.
b.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Formula used:
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 |
Median =
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 construct the pie chart or bar chart to show the proportion of given categories.
c.
![Check Mark](/static/check-mark.png)
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 explain the outcome of the analysis that is being done so far.
d.
![Check Mark](/static/check-mark.png)
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.
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Chapter 8 Solutions
PRACT. OF STAT. IN LIFE SCI.W/ACHIEVE 1
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