College

We are to determine the mean of the new set when the value 21 is included in Set A.

1. **Original Set A:**
- Number of data values, \( n = 5 \)
- Mean, \( \bar{x} = 7 \)
- Let the data values be \( x_1, x_2, x_3, x_4, x_5 \).

2. **Sum of Original Set A:**
\[
\frac{x_1 + x_2 + x_3 + x_4 + x_5}{5} = 7
\]
\[
x_1 + x_2 + x_3 + x_4 + x_5 = 35
\]

3. **New Set:**
- Includes the original 5 values and an additional value 21.
- Total number of data values = 6.

4. **Sum of New Set:**
\[
x_1 + x_2 + x_3 + x_4 + x_5 + 21 = 35 + 21 = 56
\]

5. **Mean of New Set:**
\[
\text{Mean} = \frac{56}{6}
\]

Calculate the above to find the mean of the new set.

Answer :

The new mean is approximately 9.33.

We are given Set A with 5 data values and a mean(x) = 7. To find the sum of these values, we use:

  • total sum = mean (x) × number of values (n)

Thus, the total sum of Set A is:

  • 7 × 5 = 35

Adding the new value 21 to Set A adjusts the total sum:

  • 35 + 21 = 56

The new set now contains 6 values. To find the new mean, we use:

  • new mean = total sum / new number of values

Therefore, the new mean is:

  • 56 / 6 = 9.33

The mean of the new data set after including the value 21 is approximately 9.33.

Other Questions