Answer:a) To show the cumulative frequencies for each type of battery, we can add rows to the table.
| Hours of use, hh | Type A | Type B |
|------------------|--------|--------|
| <5000 | 25 | 13 |
| 5000 | 36 | 18 |
| 6000 | 72 | 19 |
| 7000 | 121 | 23 |
| 8000 | 177 | 36 |
| 9000 | 200 | 50 |
| 10,000 | | 121 |
| 11,000 | | 177 |
| 12,000 | | 200 |
| 15,000 | | |
b) To draw a cumulative frequency curve for each battery type, we can plot the cumulative frequencies on the y-axis and the hours of use on the x-axis. We connect the points to create the curves.
c) To estimate the median for each type of battery, we find the middle value. In Type A, the median would be around 9000 hours, and in Type B, it would be around 7000 hours.
To estimate the interquartile range (IQR) for each type of battery, we find the range between the 25th and 75th percentiles. In Type A, the IQR would be around 7000-11,000 hours, and in Type B, it would be around 5000-9000 hours.
d) To draw a box plot summarizing the data for each type of battery, we need to find the minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum values. We can then create a box with lines extending from the box (whiskers) to represent the range of the data. Any outliers can be represented as individual data points outside the whiskers.
e) Using the box plots, we can compare the battery lives of the two types of batteries. We can analyze the median, interquartile range, and any outliers to determine differences in their distributions.