Question

in an effort to improve its family plans, a phone service provider wants to determine the average number of texts per day parents send to their teenagers. to collect data, company workers survey small groups of parents and guardians about the number of messages they sent to their teenager the previous day. each worker surveys 12 parents and calculates the average number of messages sent based on their sample. this line plot shows the mean number of messages from each workers sample: sample mean numbers of messages based on these statistics, what is the best estimate for the average number of messages parents and guardians send to their teenagers each day? complete the sentence. the average number of messages parents and guardians send to their teenagers each day is likely about, though the actual average number of messages could reasonably be more or less than that.

Explanation:

Step1: List all sample means

First, extract each sample mean from the line plot:
5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9

Step2: Calculate overall mean

Find the sum of all sample means, then divide by the total number of samples (16).
Sum = $5+5+6+6+6+7+7+7+7+8+8+9+9+9+9+9 = 112$
Mean = $\frac{112}{16} = 7$

Step3: Determine reasonable variation

Look at the spread of sample means: the lowest is 5, highest is 9. The typical variation around the mean of 7 is about 2 (since $7-2=5$ and $7+2=9$, which covers most sample values).

Answer:

The average number of messages parents and guardians send to their teenagers each day is likely about 7, though the actual average number of messages could reasonably be 2 more or less than that.