The set of data 9, 6, 12, 13, 9, 8, 13, 14 h and k has a mode of 9 and a median of 10. Find the value of h and k if h is less than k.

We see that the mode is 9, meaning that 9 appears the most in the set of data. Excluding h and k, 9 appears twice. 13 also appears twice. So, we can assume that either h or k has the value 9.

Now, we know that the median is 10. So, we need to sort out the numbers that we do have. In total, we have 10 numbers. Since we have an even number of numbers, the median is the average of the two middle numbers.

6, 8, 9, 9, 12, 13, 13, 14.

Since the average of the two middle numbers is 10, both middle numbers must add up to 20 because the average is the sum of both numbers divided by two.

We also know that either h or k is equal to 9. So, let's include another 9 in the set.

6, 8, 9, 9, 9, 12, 13, 13, 14.

Now, we can find two numbers that add up to 20 that can be used in this set. One of these numbers must appear in the middle set of numbers.

5 + 15

6 + 14

7 + 13

8 + 12

9 + 11

10 + 10

Let's bold some possible pairs:

5 + 15

6 + 14

7 + 13

8 + 12

9 + 11

10 + 10

Since nine is the number closest to the middle, we can find that the other number is 11. Additionally, we know that h is less than k. So:

h = 9

k = 11

Hope this helps!