Please explain 3 In a survey students are asked how many hou

3. In a survey, students are asked how many hours they study in a typical week. A five-number summary of the responses is: Min Q1 Med Q3 Max 9 14 20 60 Which interval describes the number of hours spent studying in a typical week for about 50% of the students sampled? A) 14 to 20 C B) 9 to 60 O c) 14 to 60 D) 2 to 90 Which of the following is not true: A) For graph A, the mean and median are equal B) For graph B, the data are skewed. C) For graph B, the mean is less than the median. OD) For graph c, the mean is less than the median.

Solution

3. C. 14 to 60

Each interval contains 25% of data points thus for 50% we need two intervals which are only fulfilled by C option.

4. D. For graph C, the mean is less than the median

Graph A has a symmetric distribution, so mean and median should be almost equal.

Graph B is skewed left. The mean is the balance point of the distribution. Because points further away from the balance point change the center of balance, the mean is pulled in the direction the distribution is skewed. In the given graph the distribution is skewed left , the mean would be pulled in the direction of the skewness, or be pulled toward smaller numbers.Thus mean will be smaller than median.

Apply same principle as in above case to Graph B but here the graph is skewed right so mean will be larger than median.