3. the table shows the number of hours that a grouped of students spent studying for the sat during their first week of preparation. the students each add 4 hours to their study times in the second week. what are the mean, median, mode, and range of times for the second week?

student hours
bob 19
james 10
karen 15
rosario 17
antoine 10
julio 16
maria 13

The answer is the mean, mode, and median increases by 4, the range of times is the same.

Week 1:                                              Week 2:
Student - Hours                                 Student - Hours
Bob          19                                       Bob          23
James      10                                      James       14
Karen       15                                       Karen       19
Rosario    17                                        Rosario    21
Antoine    10                                       Antoine    14
Julio         16                                       Julio         20
Maria        13                                       Maria        17

The mean is the sum of all values divided by the number of values:
Week 1: (19 + 10 + 15 + 17 + 10 + 16 + 13)/7 = 100/7 = 14.28
Week 2: (23 + 14 + 19 + 21 + 14 + 20 + 17)/7 = 128/7 = 18.28
The difference in means between Week 2 and Week 1 is 4 (18.28 - 14.28 = 4)

The median is the middle value. To calculate, first rearrange values from the lowest to the highest and then find the middle value:
Week 1: 10, 10, 13, 15, 16, 17, 19            - The median is 15.
Week 2: 14, 14, 17, 19, 20, 21, 23          - The median is 19.
The difference in medians between Week 2 and Week 1 is 4 (19 - 15 = 4)

The mode is the value that occurs most frequently.
Week 1: 10, 10, 13, 15, 16, 17, 19            - The mode is 10.
Week 2: 14, 14, 17, 19, 20, 21, 23          - The mode is 14.
The difference in modes between Week 2 and Week 1 is 4 (14 - 10 = 4)

The range of times is the difference between the highest and the lowest value.
Week 1: 10, 10, 13, 15, 16, 17, 19            - The range of times is 9 (19 - 10 = 9).
Week 2: 14, 14, 17, 19, 20, 21, 23          - The median is 9 (23 - 14 = 9).
The difference in the ranges of times between Week 2 and Week 1 is 0 (9 - 9 = 0)

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