Question

find the mean of:
38 30 17 22 22 35 5 33
12 30 20 21 1
mean =

Explanation:

Step1: Count the number of data points

We have the data set: 38, 30, 17, 22, 22, 35, 5, 33, 12, 30, 20, 21, 1. Let's count them: 1 (38) +1 (30)+1 (17)+1 (22)+1 (22)+1 (35)+1 (5)+1 (33)+1 (12)+1 (30)+1 (20)+1 (21)+1 (1) = 13 data points? Wait, wait, wait, first row: 38, 30, 17, 22, 22, 35, 5, 33 (that's 8 numbers), second row: 12, 30, 20, 21, 1 (that's 5 numbers). So total number of data points \( n = 8 + 5=13 \)? Wait, no, let's list all numbers: 38, 30, 17, 22, 22, 35, 5, 33, 12, 30, 20, 21, 1. Let's count again: 1. 38, 2. 30, 3. 17, 4. 22, 5. 22, 6. 35, 7. 5, 8. 33, 9. 12, 10. 30, 11. 20, 12. 21, 13. 1. Yes, \( n = 13 \).

Step2: Calculate the sum of all data points

Now, sum all the numbers:
\( 38 + 30 + 17 + 22 + 22 + 35 + 5 + 33 + 12 + 30 + 20 + 21 + 1 \)
Let's compute step by step:
38 + 30 = 68;
68 + 17 = 85;
85 + 22 = 107;
107 + 22 = 129;
129 + 35 = 164;
164 + 5 = 169;
169 + 33 = 202;
202 + 12 = 214;
214 + 30 = 244;
244 + 20 = 264;
264 + 21 = 285;
285 + 1 = 286.

Wait, wait, that can't be right. Wait, let's add again carefully:

First, list all numbers: 38, 30, 17, 22, 22, 35, 5, 33, 12, 30, 20, 21, 1.

Let's group them to make addition easier:

Tens and units:

38 (30+8), 30 (30+0), 17 (10+7), 22 (20+2), 22 (20+2), 35 (30+5), 5 (0+5), 33 (30+3), 12 (10+2), 30 (30+0), 20 (20+0), 21 (20+1), 1 (0+1).

Now sum the tens place: 30 + 30 + 10 + 20 + 20 + 30 + 0 + 30 + 10 + 30 + 20 + 20 + 0 = let's calculate:

305 (30,30,30,30,30? Wait no: 38 (30), 30 (30), 17 (10), 22 (20), 22 (20), 35 (30), 5 (0), 33 (30), 12 (10), 30 (30), 20 (20), 21 (20), 1 (0). So 30 appears 5 times (38,30,35,33,30) → 305=150; 10 appears 2 times (17,12) → 102=20; 20 appears 4 times (22,22,20,21) → 204=80. So total tens: 150 + 20 + 80 = 250.

Now sum the units place: 8 + 0 + 7 + 2 + 2 + 5 + 5 + 3 + 2 + 0 + 0 + 1 + 1. Let's compute:

8 + 0 = 8; 8 +7=15; 15+2=17; 17+2=19; 19+5=24; 24+5=29; 29+3=32; 32+2=34; 34+0=34; 34+0=34; 34+1=35; 35+1=36.

Now total sum = tens sum + units sum = 250 + 36 = 286? Wait, but let's check with another method. Let's add all numbers:

38 + 30 = 68;
68 +17=85;
85+22=107;
107+22=129;
129+35=164;
164+5=169;
169+33=202;
202+12=214;
214+30=244;
244+20=264;
264+21=285;
285+1=286. Yes, sum is 286.

Step3: Calculate the mean

The formula for the mean \( \bar{x} = \frac{\sum x}{n} \), where \( \sum x \) is the sum of the data points and \( n \) is the number of data points.

We have \( \sum x = 286 \) and \( n = 13 \).

So mean \( = \frac{286}{13} \). Let's compute that: 13*22 = 286. So \( \frac{286}{13} = 22 \).

Wait, that's nice. So the mean is 22.

Answer:

22