The following data identify the state of residence of a group of people where 1 = Victoria, 2 = South Australia and 3 = Western Australia. 21113131133 a Isthevariablestateofresidence,categoricalornumerical? b Constructafrequencytable(withbothnumbersandpercentages)toshowthe distribution of state of residence for this group of people. c Constructabarchartofthepercentagedfrequencytable.
Question
The following data identify the state of residence of a group of people where 1 = Victoria, 2 = South Australia and 3 = Western Australia. 21113131133 a Isthevariablestateofresidence,categoricalornumerical? b Constructafrequencytable(withbothnumbersandpercentages)toshowthe distribution of state of residence for this group of people. c Constructabarchartofthepercentagedfrequencytable.
Solution
a) The variable state of residence is categorical. This is because the numbers 1, 2, and 3 are used to represent categories (Victoria, South Australia, and Western Australia), not numerical values.
b) To construct a frequency table, we first count the number of occurrences for each state:
- Victoria (1): 5
- South Australia (2): 3
- Western Australia (3): 5
Then, we calculate the percentages by dividing the frequency of each state by the total number of people (13), and multiplying by 100:
- Victoria (1): 5/13 * 100 = 38.46%
- South Australia (2): 3/13 * 100 = 23.08%
- Western Australia (3): 5/13 * 100 = 38.46%
So, the frequency table is:
| State of Residence | Frequency | Percentage |
|---|---|---|
| Victoria | 5 | 38.46% |
| South Australia | 3 | 23.08% |
| Western Australia | 5 | 38.46% |
c) To construct a bar chart of the percentage frequency table, you would have the states of residence on the x-axis and the percentage on the y-axis. There would be three bars, one for each state. The height of each bar would correspond to the percentage of people residing in that state. Unfortunately, as a text-based AI, I'm unable to create visual content. However, you can easily create this bar chart using software like Excel or Google Sheets.
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