Question

find the mean of:
3 37 1 18 2 5 14 28
24 21 1 2
mean = 1

Explanation:

Step1: Count the number of data points

We first count how many numbers there are. Let's list them: 3, 37, 1, 18, 2, 5, 14, 28, 24, 21, 1, 2. Wait, wait, let's count again. Wait, first row: 3, 37, 1, 18, 2, 5, 14, 28 (that's 8 numbers). Second row: 24, 21, 1, 2 (that's 4 numbers). So total numbers: \(8 + 4=12\)? Wait, no, wait: 3, 37, 1, 18, 2, 5, 14, 28 (8), then 24, 21, 1, 2 (4). So total \(n = 12\)? Wait, no, let's count again: 3 (1), 37 (2), 1 (3), 18 (4), 2 (5), 5 (6), 14 (7), 28 (8), 24 (9), 21 (10), 1 (11), 2 (12). Yes, 12 numbers.

Step2: Calculate the sum of all data points

Now we sum all the numbers:
\(3 + 37 + 1 + 18 + 2 + 5 + 14 + 28 + 24 + 21 + 1 + 2\)
Let's add step by step:
\(3 + 37 = 40\)
\(40 + 1 = 41\)
\(41 + 18 = 59\)
\(59 + 2 = 61\)
\(61 + 5 = 66\)
\(66 + 14 = 80\)
\(80 + 28 = 108\)
\(108 + 24 = 132\)
\(132 + 21 = 153\)
\(153 + 1 = 154\)
\(154 + 2 = 156\)

Wait, wait, that can't be right. Wait, let's check the numbers again. Wait, 3, 37, 1, 18, 2, 5, 14, 28, 24, 21, 1, 2. Wait, maybe I missed a number? Wait, the original problem: first row: 3, 37, 1, 18, 2, 5, 14, 28 (8 numbers). Second row: 24, 21, 1, 2 (4 numbers). Wait, but maybe I miscounted. Wait, let's list all numbers:

1. 3
2. 37
3. 1
4. 18
5. 2
6. 5
7. 14
8. 28
9. 24
10. 21
11. 1
12. 2

Yes, 12 numbers. Now sum again:

\(3 + 37 = 40\)

\(40 + 1 = 41\)

\(41 + 18 = 59\)

\(59 + 2 = 61\)

\(61 + 5 = 66\)

\(66 + 14 = 80\)

\(80 + 28 = 108\)

\(108 + 24 = 132\)

\(132 + 21 = 153\)

\(153 + 1 = 154\)

\(154 + 2 = 156\)

Wait, but let's check another way. Let's group numbers:

Numbers: 1 (appears twice: 1,1), 2 (appears twice: 2,2), 3, 5, 14, 18, 21, 24, 28, 37.

So sum of 1s: \(1 + 1 = 2\)

Sum of 2s: \(2 + 2 = 4\)

Then 3, 5, 14, 18, 21, 24, 28, 37.

Sum of these: \(3 + 5 = 8\); \(8 + 14 = 22\); \(22 + 18 = 40\); \(40 + 21 = 61\); \(61 + 24 = 85\); \(85 + 28 = 113\); \(113 + 37 = 150\)

Now total sum: \(2 + 4 + 150 = 156\). Yes, that's correct.

Step3: Calculate the mean

The mean is the sum divided by the number of data points. So mean \(=\frac{\text{Sum}}{n}=\frac{156}{12}\)

\(\frac{156}{12}=13\)

Answer:

13