Question

find the mean for each data set.
age assumed office
senator | age
richard burr | 49
tammy baldwin | 50
bob corker | 54
jim inhofe | 60
dean heller | 50
joe donnelly | 57
senator | age
dan coats | 67
joe manchin | 63
marco rubio | 39
bill nelson | 58
david vitter | 43

Explanation:

Step1: Count the number of data points

First, we count how many senators (data points) there are. Let's list out the ages: 49, 50, 54, 60, 50, 57, 67, 63, 39, 58, 43. Wait, let's count the number of entries. Left table: 6 senators (Richard Burr, Tammy Baldwin, Bob Corker, Jim Inhofe, Dean Heller, Joe Donnelly). Right table: 5 senators (Dan Coats, Joe Manchin, Marco Rubio, Bill Nelson, David Vitter). So total number of data points \( n = 6 + 5 = 11 \).

Step2: Sum all the ages

Now we sum all the age values:
\( 49 + 50 + 54 + 60 + 50 + 57 + 67 + 63 + 39 + 58 + 43 \)
Let's calculate step by step:

• \( 49 + 50 = 99 \)
• \( 99 + 54 = 153 \)
• \( 153 + 60 = 213 \)
• \( 213 + 50 = 263 \)
• \( 263 + 57 = 320 \)
• \( 320 + 67 = 387 \)
• \( 387 + 63 = 450 \)
• \( 450 + 39 = 489 \)
• \( 489 + 58 = 547 \)
• \( 547 + 43 = 590 \)

Wait, that can't be right. Wait, let's re - add:

Left table ages: 49, 50, 54, 60, 50, 57. Sum of left table: \( 49+50 = 99; 99 + 54=153; 153+60 = 213; 213+50 = 263; 263+57=320 \)

Right table ages: 67, 63, 39, 58, 43. Sum of right table: \( 67+63 = 130; 130+39 = 169; 169+58 = 227; 227+43 = 270 \)

Total sum \( S=320 + 270=590 \)? Wait, no, wait 320 (left) + 270 (right) = 590? Wait, let's check the right table sum again: 67 + 63 is 130, 130+39 is 169, 169+58 is 227, 227+43 is 270. Left table: 49+50=99, +54=153, +60=213, +50=263, +57=320. Then total sum is 320 + 270 = 590. But the number of data points: left has 6, right has 5, total 11.

Wait, maybe I made a mistake in addition. Let's list all ages again: 49, 50, 54, 60, 50, 57, 67, 63, 39, 58, 43. Let's group them differently:

(49 + 51) no, better to use another approach. Let's use a calculator - like addition:

49 + 50 = 99

99 + 54 = 153

153 + 60 = 213

213 + 50 = 263

263 + 57 = 320

320 + 67 = 387

387 + 63 = 450

450 + 39 = 489

489 + 58 = 547

547 + 43 = 590. Yes, that's correct.

Step3: Calculate the mean

The formula for the mean \( \bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n} \), where \( \sum_{i = 1}^{n}x_{i} \) is the sum of all data points and \( n \) is the number of data points.

We have \( \sum x_{i}=590 \) and \( n = 11 \)

So \( \bar{x}=\frac{590}{11}\approx53.64 \) (rounded to two decimal places) or as a fraction \( \frac{590}{11}=53\frac{7}{11}\approx53.64 \)

Wait, wait, I think I made a mistake in counting the number of data points. Wait the left table: Richard Burr (49), Tammy Baldwin (50), Bob Corker (54), Jim Inhofe (60), Dean Heller (50), Joe Donnelly (57) - that's 6. Right table: Dan Coats (67), Joe Manchin (63), Marco Rubio (39), Bill Nelson (58), David Vitter (43) - that's 5. So total 11. But let's check the sum again. Let's add all numbers:

49, 50, 54, 60, 50, 57, 67, 63, 39, 58, 43.

Let's sort them to make addition easier: 39, 43, 49, 50, 50, 54, 57, 58, 60, 63, 67.

Now sum:

39 + 43 = 82

82 + 49 = 131

131 + 50 = 181

181 + 50 = 231

231 + 54 = 285

285 + 57 = 342

342 + 58 = 400

400 + 60 = 460

460 + 63 = 523

523 + 67 = 590. Yes, sum is 590. Number of data points is 11. So mean is \( \frac{590}{11}\approx53.64 \) (or exactly \( 53\frac{7}{11} \))

Answer:

The mean age is approximately \( \boldsymbol{53.64} \) (or \( \frac{590}{11} \) or \( 53\frac{7}{11} \))