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)