Choose an appropriate scale and interval size for a frequency table that will represent 2341, 2590, 2718,2453, 4160, 2635, 2734,3362, 2744, 2485, 3395, 2350, 4000, 2964, and 2600.
To choose an appropriate scale and interval size for a frequency table, we need to consider the range and distribution of the given numbers.
Step 1: Determine the range
The range is the difference between the highest and lowest values in the given data set. In this case, the highest value is 4160 and the lowest value is 2341. Therefore, the range is 4160 - 2341 = 1819.
Step 2: Determine the interval size
The interval size represents the width of each group or bin in the frequency table. It should be chosen in such a way that all the numbers can be grouped efficiently, without losing too much detail or creating very small intervals. One common approach is to select a nice round number as the interval size.
To choose an appropriate interval size, we can divide the range by the desired number of intervals or groups. However, it is important to avoid too few or too many groups. A rule of thumb is to have between 5 to 20 groups or intervals.
Let's suppose we want to have around 10 groups for this data set. We can calculate the approximate interval size as the range divided by the number of groups:
Interval size = Range / Number of groups
Interval size ≈ 1819 / 10 ≈ 182
Since we want a nice round number, we can round the interval size to the nearest convenient value, such as 200.
Step 3: Determine the scale
The scale refers to the values or numbers that will be used to label the intervals or groups on the frequency table. In this case, we can start with the first value and continue adding the interval size to get the upper value for each interval.
For example:
Interval 1: 2341 - 2540
Interval 2: 2541 - 2740
Interval 3: 2741 - 2940
...
Interval 10: 4141 - 4340
Note: The first value (2341) is included in the first interval, while the last value (4160) is included in the last interval.
By using this scale and interval size, you can construct a frequency table to represent the given data set.