In the third week, the athletes add an additional 10 min to their training times from the second week. For the second week, the mean was 38, the median was 35, the mode was 25, and the range was 30. What are the mean, median, mode and range of the times for the third week?
Let's assume that the training times for the second week are denoted by the set {x1, x2, x3, ..., xn}.
Mean: The mean is the sum of all the values divided by the total number of values. So, the mean for the second week is (x1 + x2 + x3 + ... + xn) / n = 38.
Median: The median is the middle value when the numbers are arranged in ascending order. So, the median for the second week is the 35th value.
Mode: The mode is the value that appears most frequently. So, the mode for the second week is 25.
Range: The range is the difference between the maximum and minimum values. So, the range for the second week is the difference between the largest and smallest values.
Now, in the third week, the athletes add an additional 10 minutes to their training times. So, the training times for the third week can be denoted by the set {x1 + 10, x2 + 10, x3 + 10, ..., xn + 10}.
Mean: The mean for the third week is the sum of all the values divided by the total number of values. So, the mean for the third week is (x1 + 10 + x2 + 10 + x3 + 10 + ... + xn + 10) / n = 38 + 10 = 48.
Median: To find the median for the third week, we need to arrange the values in ascending order. So, the median for the third week will be the (n+1)/2 th value.
Mode: The mode for the third week will be the same as the mode for the second week, i.e., 25.
Range: The range for the third week will be the difference between the largest and smallest values.
Therefore, the mean, median, mode, and range for the third week are 48, median value, 25, and range value respectively.