Question

There are 12 bags of apples on a market stall.

The mean number of apples in each bag is 8.
The table shows the number of apples
in 11 of the bags.
Calculate the number of apples in the 12th bag.
Optional working
Ansv apples
+
Number of
apples
6
7
8
9
10
Frequency
1
4
2
3
1

Answer 1

96 apples in all 12 bags

Answer 2

Explanation:

To calculate the number of apples in the 12th bag, we need to use the information given about the mean number of apples and the frequency of each bag.

Given data:

- Mean number of apples in each bag: 8

- Frequency distribution for 11 bags:

- Number of apples: 6, Frequency: 1

- Number of apples: 7, Frequency: 4

- Number of apples: 8, Frequency: 2

- Number of apples: 9, Frequency: 3

- Number of apples: 10, Frequency: 1

To find the number of apples in the 12th bag, we can calculate the total sum of apples in the 11 bags and subtract it from the expected total sum based on the mean.

Step-by-step calculation:

1. Calculate the total sum of apples in the 11 bags:

(6 * 1) + (7 * 4) + (8 * 2) + (9 * 3) + (10 * 1) = 6 + 28 + 16 + 27 + 10 = 87.

2. Calculate the expected total sum based on the mean:

Mean number of apples (8) multiplied by the total number of bags (12):

8 * 12 = 96.

3. Calculate the number of apples in the 12th bag:

Number of apples in the 12th bag = Expected total sum - Total sum of the 11 bags:

96 - 87 = 9.

Therefore, the number of apples in the 12th bag is 9.