0000:00:00:00:00Start4Number 4ExplanationFrom the data 444, 555, 555, 222, 333, 111, 666, which statements are true? Median =4= 4=4. Range =6= 6=6. Range −-− median =1= 1=1. Mean =4.5= 4.5=4.5. (1)(1)(1), (2)(2)(2), and (3)(3)(3) ONLY are correct.(1)(1)(1) and (3)(3)(3) ONLY are correct.(2)(2)(2) and (4)(4)(4) ONLY are correct.ONLY (4)(4)(4) is correct.ALL choices are correct.ExplanationSort the data from smallest to largest: 1,2,3,4,5,5,61, 2, 3, 4, 5, 5, 61,2,3,4,5,5,6 Number of data points n=7n = 7n=7. Statement 1 Analysis The median is the n+12=82=4\frac{n+1}{2} = \frac{8}{2} = 42n+1=28=4-th value. The 444-th value is 444. Me=4Me = 4Me=4 Statement 111 is CORRECT. Statement 2 Analysis The range is the difference between the maximum and minimum values. Range=xmax−xmin=6−1=5Range = x_{max} - x_{min} = 6 - 1 = 5Range=xmax−xmin=6−1=5 Statement 222 is INCORRECT (should be 555, not 666). Statement 3 Analysis Difference between range and median: Range−Me=5−4=1Range - Me = 5 - 4 = 1Range−Me=5−4=1 Statement 333 is CORRECT. Statement 4 Analysis The mean (xˉ\bar{x}xˉ) is the sum of all data divided by the number of data points. xˉ=1+2+3+4+5+5+67=267=357\bar{x} = \frac{1 + 2 + 3 + 4 + 5 + 5 + 6}{7} = \frac{26}{7} = 3\frac{5}{7}xˉ=71+2+3+4+5+5+6=726=375 The value 3573\frac{5}{7}375 is not equal to 4.54.54.5. Statement 444 is INCORRECT. Conclusion The correct statements are (1)(1)(1) and (3)(3)(3).
4Number 4ExplanationFrom the data 444, 555, 555, 222, 333, 111, 666, which statements are true? Median =4= 4=4. Range =6= 6=6. Range −-− median =1= 1=1. Mean =4.5= 4.5=4.5. (1)(1)(1), (2)(2)(2), and (3)(3)(3) ONLY are correct.(1)(1)(1) and (3)(3)(3) ONLY are correct.(2)(2)(2) and (4)(4)(4) ONLY are correct.ONLY (4)(4)(4) is correct.ALL choices are correct.ExplanationSort the data from smallest to largest: 1,2,3,4,5,5,61, 2, 3, 4, 5, 5, 61,2,3,4,5,5,6 Number of data points n=7n = 7n=7. Statement 1 Analysis The median is the n+12=82=4\frac{n+1}{2} = \frac{8}{2} = 42n+1=28=4-th value. The 444-th value is 444. Me=4Me = 4Me=4 Statement 111 is CORRECT. Statement 2 Analysis The range is the difference between the maximum and minimum values. Range=xmax−xmin=6−1=5Range = x_{max} - x_{min} = 6 - 1 = 5Range=xmax−xmin=6−1=5 Statement 222 is INCORRECT (should be 555, not 666). Statement 3 Analysis Difference between range and median: Range−Me=5−4=1Range - Me = 5 - 4 = 1Range−Me=5−4=1 Statement 333 is CORRECT. Statement 4 Analysis The mean (xˉ\bar{x}xˉ) is the sum of all data divided by the number of data points. xˉ=1+2+3+4+5+5+67=267=357\bar{x} = \frac{1 + 2 + 3 + 4 + 5 + 5 + 6}{7} = \frac{26}{7} = 3\frac{5}{7}xˉ=71+2+3+4+5+5+6=726=375 The value 3573\frac{5}{7}375 is not equal to 4.54.54.5. Statement 444 is INCORRECT. Conclusion The correct statements are (1)(1)(1) and (3)(3)(3).
