Question

to determine the number of apples people typically eat in a week, the blue mountain apple growers association solicits volunteers to randomly survey 10 friends and family members about how many apples they ate the previous week. this line plot shows the mean number of apples eaten from each volunteers sample: sample mean numbers of apples (line plot with x - axis from 0 to 10, marked at 0,2,4,6,8,10; blue dots representing sample means). based on these statistics, what is the best estimate for the average number of apples eaten in a week? complete the sentence. the average number of apples eaten in a week is likely to be about ___, though it could reasonably be anywhere between. options for the first blank (and related to the second part): 2, 4, 6, 8

Explanation:

Step1: Count total sample means

First, tally all the data points:

• At 2: 3 + 10 = 13
• At 3: 5 + 10 = 15
• At 4: 2 + 5 + 1 = 8
• At 5: 1
• At 6: 10
• At 9: 1

Total points: $13 + 15 + 8 + 1 + 10 + 1 = 48$

Step2: Calculate weighted mean

Multiply each value by its count, sum, then divide by total points:
$$\text{Weighted Mean} = \frac{(2 \times 13) + (3 \times 15) + (4 \times 8) + (5 \times 1) + (6 \times 10) + (9 \times 1)}{48}$$
$$= \frac{26 + 45 + 32 + 5 + 60 + 9}{48}$$
$$= \frac{177}{48} = 3.6875 \approx 4$$

Step3: Identify reasonable range

The data spans from 2 to 9, but the cluster is between 2 and 6. The most reasonable range is the spread of the majority of data points.

Answer:

The average number of apples eaten in a week is likely to be about 4, though it could reasonably be anywhere between 2 and 6.