Final answer:
The percentage of data that lies within ±1 from the given set [5, 21, 17, 24, 15, 28, 10] is 28.57%.
Step-by-step explanation:
To find the percentage of data that lies within ±1 from the given set [5, 21, 17, 24, 15, 28, 10], we need to count the number of values that fall within the range of (mean - 1) and (mean + 1), and divide it by the total number of values in the set.
In this case, the mean of the set is (5+21+17+24+15+28+10)/7 = 16. So, the range for ±1 from the mean is (16 - 1) and (16 + 1), which is 15 and 17.
Looking at the set, we can see that two values, 15 and 17, fall within this range. Therefore, the percentage of data that lies within ±1 from the given set is (2/7) * 100 = 28.57%.
Hence, the correct option is d) 28.57%.