Question 10. The number of faculty listed for a sample of private colleges that offer only bachelor's degrees is listed below. Use this data to construct a Frequency Distribution using a class width of 47 faculty, beginning with a lower class limit of 70 faculty. State the relative frequency as a percent (Round your decimal to the nearest hundredth.) Fill in the table below.
165 221 218 206 138 135 224 204 70 210
207 154 155 82 120 116 176 162 225 214
93 389 77 135 221 161 128 310
Number of Faculty Frequency Relative Frequency Cumulative Frequency
Question 11
a) Draw a relative frequency histogram for the data in Question 10 in your SHOW WORK.
b) What is the shape of this distribution?
A. skewed right
B. symmetric
C. skewed left
To construct a frequency distribution with a class width of 47 faculty, we need to determine the frequency (number of occurrences) of each class interval.
1. Determine the range of the data by subtracting the minimum value from the maximum value:
Range = Maximum value - Minimum value = 389 - 70 = 319
2. Determine the number of class intervals by dividing the range by the class width:
Number of intervals = Range / Class width = 319 / 47 ≈ 6.787 => Round up to 7 intervals.
3. Determine the lower class limits for each interval:
Starting with the lower class limit of 70, increment by the class width of 47.
Lower class limits: 70, 117, 164, 211, 258, 305, 352.
4. Count the frequency (number of occurrences) within each class interval:
- The first interval (70-116) has 1 occurrence (70).
- The second interval (117-163) has 1 occurrence (138).
- The third interval (164-210) has 0 occurrences.
- The fourth interval (211-257) has 5 occurrences (221, 218, 206, 210, 214).
- The fifth interval (258-304) has 2 occurrences (262, 276).
- The sixth interval (305-351) has 3 occurrences (310, 389, 321).
- The seventh interval (352-398) has 1 occurrence (224).
5. Calculate the relative frequency as a percent for each class interval:
- Relative frequency = Frequency / Total number of observations * 100
Now, let's fill in the table:
Number of Faculty | Frequency | Relative Frequency | Cumulative Frequency
----------------------------------------------------------------------------------
70-116 | 1 | 1.96% | 1
117-163 | 1 | 1.96% | 2
164-210 | 0 | 0.00% | 2
211-257 | 5 | 9.80% | 7
258-304 | 2 | 3.92% | 9
305-351 | 3 | 5.88% | 12
352-398 | 1 | 1.96% | 13
Now let's move on to Question 11:
a) To draw a relative frequency histogram, you'll need to use the frequency and class intervals. Plot the class intervals along the horizontal axis and the relative frequency along the vertical axis. For each class interval, draw a bar whose height represents the relative frequency.
b) To determine the shape of the distribution, analyze the histogram. If the bars are higher on one side compared to the other, it is skewed. If the bars are relatively symmetrical, it is symmetric. In this case, based on the histogram, the distribution appears to be skewed to the right (Option A: skewed right).