Question

3. The data below shows the masses (in kg) at birth of forty babies born at a

maternity home I a week. 3.2 3.0 3.8 4.2 2.8 3.6 2.8 3.5
4.6 4.3 3.4 3.5 3.4 2.7 4.6 3.9
2.9 3.7 4.3 3.7 3.1 3.0 3.4 2.8
3.7 3.3 3.3 2.7 3.7 4.4 3.1 3.4
2.9 3.8 4.0 2.8 3.6 3.3 3.0 3.2
(a) Construct a frequency table using the class intervals: 2.25-2.75, 2.75- 5.25, 3.25-3.75, 3.75-4.25 and 4.25-4.75kg
(b) Estimate :
(i) the median of the distribution
(ii) the mode of the distribution
(iii) the mean of the distribution

Answer 1

Therefore, the mean of the distribution is 3.495 kg.

Explanation:

Based on the data provided, a frequency table was constructed using the given class intervals:

Class Interval | Frequency
2.25-2.75 kg | 2
2.75-3.25 kg | 4
3.25-3.75 kg | 13
3.75-4.25 kg | 12
4.25-4.75 kg | 9

To estimate the median of the distribution, we need to arrange the data in ascending order:

2.7 2.8 2.8 2.9 2.9 3.0 3.0 3.1
3.1 3.2 3.3 3.3 3.4 3.4 3.4 3.5
3.5 3.6 3.6 3.7 3.7 3.7 3.8 3.8
3.9 4.0 4.2 4.3 4.3 4.4 4.6 4.6

The median is the middle value of the data set, which is 3.5 kg.

To estimate the mode of the distribution, we look for the class interval with the highest frequency. In this case, the class interval with the highest frequency is 3.25-3.75 kg, with a frequency of 13. Therefore, the mode of the distribution is 3.25-3.75 kg.

To estimate the mean of the distribution, we use the formula:

mean = (sum of all values) / (total number of values)

Using the data provided, we get:

mean = (3.2 + 3.0 + 3.8 + 4.2 + 2.8 + 3.6 + 2.8 + 3.5 + 4.6 + 4.3 + 3.4 + 3.5 + 3.4 + 2.7 + 4.6 + 3.9 + 2.9 + 3.7 + 4.3 + 3.7 + 3.1 + 3.0 + 3.4 + 2.8 + 3.7 + 3.3 + 3.3 + 2.7 + 3.7 + 4.4 + 3.1 + 3.4 + 2.9 + 3.8 + 4.0 + 2.8 + 3.6 + 3.3 + 3.0 + 3.2) / 40

mean = 3.495 kg

Therefore, the mean of the distribution is 3.495 kg.