275, 284, 288, 296,322,323,325,366,374. If number 275 changes to 320 , a) what happens to median? b) what happens to mean _ increases by how much?

Let's tackle this step by step.

### 1. **Original Numbers:**
The given set of numbers is:
\[ 275, 284, 288, 296, 322, 323, 325, 366, 374 \]

#### a) **Finding the Median (before the change):**
- **Sorted order:** The numbers are already sorted.
- The median is the middle number. Since there are 9 numbers, the median will be the 5th number:
  \[
  \text{Median} = 322
  \]

#### b) **Finding the Mean (before the change):**
The mean is the sum of all numbers divided by the total count.
\[
\text{Mean} = \frac{275 + 284 + 288 + 296 + 322 + 323 + 325 + 366 + 374}{9} = \frac{2853}{9} = 317
\]

---

### 2. **After Changing 275 to 320:**
The new set of numbers becomes:
\[ 320, 284, 288, 296, 322, 323, 325, 366, 374 \]

#### a) **New Median:**
- **Sorted order:** The new sorted set is:
  \[
  284, 288, 296, 320, 322, 323, 325, 366, 374
  \]
- The middle number is still the 5th one:
  \[
  \text{New Median} = 322
  \]
- **Result:** The median **remains unchanged**.

#### b) **New Mean:**
The new sum is:
\[
\text{New Sum} = 320 + 284 + 288 + 296 + 322 + 323 + 325 + 366 + 374 = 2898
\]
\[
\text{New Mean} = \frac{2898}{9} = 322
\]
- **Change in Mean:** The mean increased from **317 to 322**. Hence, the increase is:
\[
322 - 317 = 5
\]
- **Result:** The mean increases by **5**.

---

### Summary:
- **a) Median:** The median **remains unchanged** at 322.
- **b) Mean:** The mean **increases by 5**.

Would you like more details on any of the steps? Here are 5 related questions for practice:
1. How do you find the mode of a set of numbers?
2. What happens to the median if a number in the middle is changed?
3. How does removing an outlier affect the mean?
4. Can the median ever be larger than all the numbers in a set?
5. How is the weighted mean different from the arithmetic mean?

**Tip:** Changing a number far from the median typically affects the mean more than the median!

275, 284, 288, 296, 322, 323, 325, 366, 374. If number 275 changes to 320, a) what happens to the median? b) what happens to the mean _ increases by how much?

Discover how changing a number in the dataset 275, 284, 288, 296, 322, 323, 325, 366, 374 affects the mean and median. Learn how the mean increases by 5 while the median remains unchanged at 322. Suitable for students in Grades 6-8.

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